Edward F. Assmus, Jr (19311998)
Ed Assmus died suddenly at the age of 66, on the evening of Wednesday
18 March 1998 while participating in the meeting on Designs and Codes at
Oberwolfach, Germany. Shocked and saddened, the other participants
held a memorial service for him on the following day and brought the
meeting to a swift close.
Ed retired from his position at Lehigh University in Bethlehem,
Pennsylvania, in July 1994, after 28 years as a member of the faculty
there. During that time he had become worldrenowned for his work in
codes and designs. When he started his research in codes, in 1962,
most mathematicians were unacquainted with the subject, and his work
did much to make coding theory recognized in the mathematical world.
Born on 19 April 1931 at Nutley, New Jersey, he was educated at
Oberlin College and at Harvard University, where he obtained his
doctorate in 1958. From 1958 to 1962 he was employed as Office of
Naval Research Associate and Ritt Instructor at Columbia University.
After that, and until 1966, he was a Lecturer at Wesleyan University.
It was during that period that his interests shifted from homological
algebra to applied combinatorics. He joined the faculty at Lehigh
University in 1966 as associate professor and was promoted to
professor in 1970. In May 1993 he was awarded the title of
Distinguished Professor. He retired in July 1994. During his time at
Lehigh he had many productive visiting positions in the U.S.A.,
Canada, and Europe. His excellence as a lecturer made him in demand
as an invited speaker at many universities and conferences; he gave
over 100 invited lectures on 80 separate occasions in mathematics
departments and universities in the United States and in nine other
countries. His publication list includes approximately 60 research
papers and many book reviews. He had eleven doctoral
students at Lehigh:
E. P. Shaughnessy (1969),
M. M. Guza (1973),
H. E. Sachar (1973),
D. P. Maher (1975),
J. A. Mezzaroba (1975),
C. J. Salwach (1976),
B. R. Andriamanalimanana (1979),
J. E. N. Sardi (1980),
S. T. Dougherty (1992),
K. J. Rose (1993),
J. C. Janssen (1993).
He was a reviewer for both Mathematical Reviews and Zentralblatt
für Mathematik, and wrote occasional book reviews for periodicals.
He was a member of the editorial board of the journals Designs, Codes
and Cryptography, and the Electronic Journal of Combinatorics, and
refereed for various mathematical journals, including Journal of
Combinatorial Theory, Information and Control, Discrete Mathematics,
American Mathematical Monthly, and IEEE Transactions on Information
Theory. He was a member of the American Mathematical Society, the
London Mathematical Society, the Society for Industrial and Applied
Mathematics, the Mathematical Association of America, the American
Association for the Advancement of Science, and the Institute of
Combinatorics and its Applications.
After his retirement, he remained professionally active, traveling
extensively and often invited to spend extended periods at various
prestigious research establishments. In particular, he frequently
spent some months at INRIA, near Versailles, working with Paul Camion
and Pascale Charpin at Projet Codes.
Ed's doctoral thesis, under John Tate at Harvard in 1958, was on
the homology of local rings. He proved that Tor^{R}(K,K), where R is
a local ring and K the residue class field, is a Hopf algebra. Although
much more is now known about these algebras, his results [[1]]
are still cited in the homological algebra literature.
Within a few years his interests had changed, and he started to work
on the then somewhat unfashionable area of algebraic coding theory. A
long collaboration with H. F. Mattson, jr.,
resulted in a series of papers on the
relationship between algebraic coding theory and classical
combinatorial theory. Possibly the best known of the joint papers was
[[16]], where they showed how combinatorial information can
be extracted from codes. In particular, the central theorem of that
paper shows how vectors of a fixed weight in a linear code can produce
a tdesign; this frequently quoted result is referred to as
the ``AssmusMattson Theorem".
From 1962 to 1972, Ed and Mattson produced an annual report for the
Air Force contract under which they worked. These reports, some of
which are included in the list of publications, contained all their
work for the year, and some parts were published in journals. The
reports, which were widely circulated, and the expository paper
[[23]] which explained some of their results, helped to
interest mathematicians in coding theory. During the same period
there were monthly meetings of a group centering around Andy Gleason,
with other members Gene Prange, Vera Pless, John N. Pierce, Skip
Mattson, and Ed. Usually guests also came, and frequent visitors were
Elwyn Berlekamp, Jessie MacWilliams, and Neil Sloane. One of the
highlights was Ed's presentation in spring 1970 of his results on the
plane of order 10 to an appreciative audience of `members' and guests
from Bell Labs.
Ed's interest in the relationship between codes and designs continued,
and at a lecture in Oberwolfach in spring 1970, he pointed out the
connection between the problem of the existence of a projective plane
of order 10 and the existence of certain doublyeven, selfdual binary
codes. His approach [[18],[21]], extended by several subsequent
researchers, was the key to the proof by Lam^{1} et al. (by computer, in 1989) that no
such plane exists. Somewhat more generally, he established connections
between symmetric designs of even order and their ovals on the one
hand, and selforthogonal codes on the other; this was joint work with
J. H. van Lint [[32]].
A more recent collaboration with J. D. Key commenced in 1986 with the
publication [[41]], in which a simple method for extending some
Steiner 2designs using ovals was described, producing a new class of
Steiner 3designs. This collaboration continued with further research
into codes associated with designs, and the attempt to use coding
theory as a classifying tool for the designs. This resulted in a
series of papers
[[45],[46],[47],[48],[52],[56]] on
codes and planes, unitals, and Hadamard designs. The culmination of
the joint work was a research monograph [[51]] on the link
between designs and codes. A jointly written chapter [[59]]
on the codes from finite geometries, for a handbook of coding theory
edited by V. Pless and W. Huffman, is due to appear in 1998. This dealt
exclusively with generalized ReedMuller codes and their duals, and
expanded the results described
in Chapter 5 of the monograph [[51]]. The
paper [[56]] updates some of the results and questions posed
in [[51]] that were subsequently answered.
The most recent work includes a full classification of binary codes
from Steiner triple systems [[54],[58]] and a paper defining
a category associated with linear codes [[57]]. His last paper
concerned binary codes associated with oddorder nets, and is joint
with A. Drisko [[60]]. This was the work he spoke about in his
excellent talk at Oberwolfach in March, the day before his death.
Over the years, his many papers show evidence of his many collaborations
other than those mentioned above: he published jointly with most of his
doctoral students, and with J. J. Florentin, M. T. Hermoso,
J. M. Goethals, V. Pless, and A. R. Prince.
Ed is survived by his wife Susan, daughter Alexi, and son Richard. He
will be sorely missed by his friends and colleagues all over the
world.
References
 [[1]]

E. F. Assmus, Jr.
On the homology of local rings.
Illinois J. Math., 3:187199, 1959.
 [[2]]

E. F. Assmus, Jr.
Betti numbers of local rings.
Reports of the seminar on algebra
Summer 1959, Technical Report No. 2,
Contract NONR  2121(12) between the
office of Naval Research and the University of Chicago.
 [[3]]

E. F. Assmus, Jr.
A continuous function.
Amer. Math. Monthly, 69:647, 1962.
 [[4]]

E. F. Assmus, Jr. and H. F. Mattson.
Errorcorrecting codes: an axiomatic approach.
Inform. and Control, 6:315330, 1963.
 [[5]]

E. F. Assmus, Jr.
On some mathematical aspects of Production from Consumption.
Public Finance, XX:199202, 1965.
 [[6]]

E. F. Assmus, Jr. and H. F. Mattson, Jr.
Perfect codes and the Mathieu groups.
Arch. Math., 17:122135, 1966.
 [[7]]

E. F. Assmus, Jr. and H. F. Mattson, Jr.
Disjoint Steiner systems associated with the Mathieu groups.
Bull. Amer. Math. Soc., 72:843845, 1966.
 [[8]]

E. F. Assmus, Jr. and H. F. Mattson, Jr.
On the number of inequivalent Steiner triple systems.
J. Combin. Theory, 1:301305, 1966.
 [[9]]

E. F. Assmus, Jr. and H. F. Mattson, Jr.
On tactical configurations and errorcorrecting codes.
J. Combin. Theory, 2:243257, 1967.
 [[10]]

E. F. Assmus, Jr. and H. F. Mattson, Jr.
Intersections of cyclic Hamming codes.
J. Combin. Theory, 3:307, 1967.
 [[11]]

E. F. Assmus, Jr., H. F. Mattson, Jr., and R. J. Turyn.
Research to Develop the Algebraic Theory of Codes.
Applied Research Laboratory, Sylvania Electronic Systems, June 1967.
No. AFCRL670365. Contract No. AF19(628)5998.
 [[12]]

E. F. Assmus, Jr. and J. J. Florentin.
Algebraic Machine Theory and Logical Design.
Algebraic Theory of Machines, Chapter 2, pages 1535, edited by
Michael Arbib, Academic Press, 1968.
 [[13]]

E. F. Assmus, Jr.
On the optimality of cyclic codes.
Proceedings of the Hawaii
International Conference on System Sciences
University
of Hawaii Press, 1968.
 [[14]]

E. F. Assmus, Jr. and H. F. Mattson, Jr.
Some (3p,p) codes.
Information Processing 68, 1:205209, 1969.
 [[15]]

E. F. Assmus, Jr. and H. F. Mattson, Jr.
On the automorphism groups of PaleyHadamard matrices.
Combinatorial Mathematics and its
Applications, Chapter 6, University of North Carolina Press, 1969.
 [[16]]

E. F. Assmus, Jr. and H. F. Mattson, Jr.
New 5designs.
J. Combin. Theory, 6:122151, 1969.
 [[17]]

E. F. Assmus, Jr.
The Projective Plane of Order 10?
Mathematisches Forschungsinstitut, Oberwolfach, Germany,
April 1, 1970
 [[18]]

E. F. Assmus, Jr. and H. F. Mattson, Jr.
On the possibility of a projective plane of order 10.
Algebraic Theory of Codes II.
GTE Sylvania, October, 1970. AFCRL710013. Contract No.
F1962869C0068.
 [[19]]

E. F. Assmus, Jr. and H. F. Mattson, Jr.
On weights in quadraticresidue codes.
Discrete Math., 3:120, 1972.
 [[20]]

E. F. Assmus, Jr. and H. F. Mattson, Jr.
Contractions of selforthogonal codes.
Discrete Math., 3:2132, 1972.
 [[21]]

E. F. Assmus, Jr., H. F. Mattson, Jr. and Marcia Guza.
SelfOrthogonal Steiner systems and projective planes.
Math. Z., 138:8996, 1974.
 [[22]]

E. F. Assmus, Jr. and Maria Teresa Hermoso.
Nonexistence of Steiner systems of type S(d1,d,2d).
Math. Z., 138:171172, 1974.
 [[23]]

E. F. Assmus, Jr. and H. F. Mattson, Jr.
Coding and combinatorics.
Siam Review, 16:349388, 1974.
 [[24]]

E. F. Assmus, Jr. and H. F. Mattson, Jr.
Some 3errorcorrecting BCH codes have covering radius 5.
IEEE Trans. Inform. Theory, 22:348349, 1976.
 [[25]]

E. F. Assmus, Jr., H. F. Mattson, Jr. and Howard E. Sachar.
A new form of the squareroot bound.
SIAM J. Appl. Math., 30:352354, 1976.
 [[26]]

E. F. Assmus, Jr., J.M. Goethals and H. F. Mattson, Jr.
Generalized tdesigns and majority decoding of linear codes.
Information and Control, 32:4360, 1976.
 [[27]]

E. F. Assmus, Jr., Joseph A. Mezzaroba, and Chester J. Salwach.
Planes and biplanes.
In M. Aigner, editor, Higher Combinatorics, pages 205212. D.
Reidel, 1977.
Proceedings of the NATO Conference, Berlin 1976.
 [[28]]

E. F. Assmus, Jr. and Howard E. Sachar.
Ovals from the point of view of coding theory.
In M. Aigner, editor, Higher Combinatorics, pages 213216. D.
Reidel, 1977.
Proceedings of the NATO Conference, Berlin 1976.
 [[29]]

E. F. Assmus, Jr. and D. P. Maher.
Nonexistence proofs for projective designs.
Amer. Math. Monthly, 85:110112, 1978.
 [[30]]

E. F. Assmus, Jr. and H. F. Mattson, Jr.
The weightdistribution of a coset of a linear code.
IEEE Trans. Inform. Theory, IT24:497, 1978.
 [[31]]

E. F. Assmus, Jr. and Chester J. Salwach.
The (16,6,2) designs.
Internat. J. Math. & Math. Sci., 2:261281, 1979.
 [[32]]

E. F. Assmus, Jr. and J. H. van Lint.
Ovals in projective designs.
J. Combin. Theory, Ser. A, 27:307324, 1979.
 [[33]]

E. F. Assmus, Jr. and J. E. Novillo Sardi
Generalized Steiner systems of type 3(v, 4,6, 1).
Proceedings of the Finite Geometries and Designs
Conference
Sussex June 1980, Cambridge University Press, 1981, 1621.
 [[34]]

E. F. Assmus, Jr. and Vera Pless.
On the covering radius of extremal selfdual codes.
IEEE Trans. Inform. Theory, IT29:359363, 1983.
 [[35]]

E. F. Assmus, Jr.
Applications of algebraic coding theory to finite geometric problems.
In N. L. Johnson et al., editor, Finite Geometries, pages
2332. New York: M. Dekker, 1983.
Lecture Notes in Pure and Applied Math., 82.
 [[36]]

E. F. Assmus, Jr.
Estensioni per ovali di piani e bipiani e questioni
collegate.
Lecture Notes of
lectures delivered in the Seminario di Geometrie
Combinatorie diretto da G. Tallini, Universita Degli Studi di
Roma, Instituto ``Guido Castelnuovo'', no. 45, Giugno 1983.
 [[37]]

E. F. Assmus, Jr.
The binary code arising from a 2design with a nice collection of
ovals.
IEEE Trans. Inform. Theory, 29:367369, 1983.
 [[38]]

E. F. Assmus, Jr.
Pi
Amer. Math. Monthly, 92:213214, 1985
 [[39]]

E. F. Assmus, Jr.
The nonexistence of an ovalextendable (56, 11, 2) design.
Journal of Geometry, 24:168174, 1985
 [[40]]

E. F. Assmus, Jr.
Extending planar spaces.
International Conference on Finite Geometry and Combinatorics, Deinze
(Ghent), 1986.
 [[41]]

E. F. Assmus, Jr. and J. D. Key.
On an infinite class of Steiner systems with t = 3 and k = 6.
J. Combin. Theory, Ser. A, 42:5560, 1986.
 [[42]]

E. F. Assmus, Jr.
Biplanes in Planes.
Congr. Numer., 60:279294, 1987.
 [[43]]

E. F. Assmus, Jr.
The coding theory of finite geometries and designs.
Lecture Notes in Computer Science 357:16, 1989.
 [[44]]

E. F. Assmus, Jr.
On the theory of designs.
In J. Siemons, editor, Surveys in Combinatorics, 1989, pages
121. Cambridge: Cambridge University Press, 1989.
London Mathematical Society Lecture Note Series 141.
 [[45]]

E. F. Assmus, Jr. and J. D. Key.
Arcs and ovals in the hermitian and Ree unitals.
European J. Combin., 10:297308, 1989.
 [[46]]

E. F. Assmus, Jr. and J. D. Key.
Affine and projective planes.
Discrete Math., 83:161187, 1990.
 [[47]]

E. F. Assmus, Jr. and J. D. Key.
Baer subplanes, ovals and unitals.
In Dijen RayChaudhuri, editor, Coding Theory and Design Theory,
Part I, pages 18. New York: SpringerVerlag, 1990.
The IMA Volumes in Mathematics and its Applications, Volume 20.
 [[48]]

E. F. Assmus, Jr. and J. D. Key.
Translation planes and derivation sets.
J. Geom., 37:316, 1990.
 [[49]]

E. F. Assmus, Jr. and Alan R. Prince.
Biplanes and near biplanes.
J. Geom., 40:114, 1991.
 [[50]]

E. F. Assmus, Jr.
On the ReedMuller codes.
Discrete Math., 106/107:2533, 1992.
 [[51]]

E. F. Assmus, Jr. and J. D. Key.
Designs and their Codes.
Cambridge University Press, 1992.
Cambridge Tracts in Mathematics, Vol. 103 (Second printing with
corrections, 1993).
 [[52]]

E. F. Assmus, Jr. and J. D. Key.
Hadamard matrices and their designs: a codingtheoretic approach.
Trans. Amer. Math. Soc., 330:269293, 1992.
 [[53]]

Edward F. Assmus, Jr. and Jennifer D. Key.
Codes and finite geometries.
Technical report, INRIA, 1993.
Report No. 2027.
 [[54]]

E. F. Assmus, Jr.
On 2ranks of Steiner triple systems.
Electron. J. Combin., 2:Research Paper 9, 1995.
 [[55]]

E. F. Assmus, Jr.
On Berman's characterization of the ReedMuller codes.
J. Statist. Plann. Inference, 56:1721, 1996.
 [[56]]

E. F. Assmus, Jr. and J. D. Key.
Designs and codes: an update.
Des. Codes Cryptogr., 9:727, 1996.
 [[57]]

E. F. Assmus, Jr.
The category of linear codes.
IEEE Trans. Inform. Theory, 44:612629, 1998.
 [[58]]

E. F. Assmus, Jr.
Linearly derived Steiner triple systems.
Des. Codes Cryptogr., 13:119, 1998.
 [[59]]

E. F. Assmus, Jr. and J. D. Key.
Polynomial codes and finite geometries.
Chapter in Handbook of Coding Theory, edited by V. Pless
and
W. C. Huffman.
Elsevier. To appear 1998
 [[60]]

E. F. Assmus, Jr. and A. Drisko.
Binary codes of oddorder nets.
Submitted.
Footnotes:
^{1}C. W. H. Lam,
The search for a finite projective plane of order 10, Amer. Math. Monthly, 98 (1992) 305318.
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