A Tribute to Vera Pless (1931–2020)
By W. Cary Huffman
Professor Emeritus
Department of Mathematics and Statistics
Loyola University of Chicago
[email protected]
Vera Stepen Pless passed away at her home in Oak Park, Illinois on March 2, 2020, a few days short of her 89th birthday. She was a leading expert in the theory of errorcorrecting codes, being one of the very few women doing research in coding theory in its early years.
Vera Stepen was born in Chicago, Illinois on March 5, 1931, the daughter of Russian Jewish immigrants. She left high school after two years to pursue a “great books” program at the University of Chicago, graduating in three years. In 1952 she married Irwin Pless and completed an M.A. also from the University of Chicago. Subsequently she joined a physics group at the university but soon afterwards received a fellowship from Northwestern University. Vera moved with her husband to Boston and completed her Ph.D. longdistance as a ring theory student of Alex Rosenberg, defending her dissertation [10, 11] two weeks before the birth of her first child.
In 1963 Vera joined the Air Force Cambridge Research Laboratory (AFCRL) to work in the new research area of errorcorrecting codes and continued to work there for ten years, resigning after the Department of Defense was prohibited from doing pure research. Upon leaving the AFCRL, she became a research associate at the Massachusetts Institute of Technology. In 1975 Vera was appointed full professor in the Department of Mathematics, Statistics and Computer Science at the University of Illinois Chicago where she taught until her retirement in 2006.
Vera Pless made significant, original, and lasting contributions to the study of error correcting codes. In 1963, she published her first major work [12] in coding theory presenting what are now called the Pless power moments relating the weight distributions of a linear code to that of its dual. These power moments are equivalent to the MacWilliams identities published by F. Jessie MacWilliams [9] in the same year. Over the next few years, she helped establish the uniqueness of the Golay codes [14] and discovered what are now called the Pless symmetry codes [16].
Vera was among the first to explore the classification of maximal selforthogonal and selfdual codes with her presentation of these binary codes up to length 20 in [15]. She followed this with the classification of selfdual codes of moderate lengths over various fields in succeeding publications, some with authors such as John H. Conway and Neil J. A. Sloane; see for example [3]. She developed mass formulas [13] that verify completeness of the classifications; she even modified the GROUP computer system to create the Combinatorial and Algebraic Machine Aided Computation (CAMAC) system [17] to assist in the computations.
In addition to the Pless symmetry codes, she discovered generalizations of quadratic residue codes called duadic codes [8] and Qcodes [18]. Vera together with Richard A. Brualdi developed greedy codes [2], a generalization of lexicodes. Vera even delved into codes over rings studying cyclic codes over Z _{ 4 } with Patrick Solé and her Ph.D. student Zhongqiang Qian in [21, 22]. Vera also tackled questions as diverse as covering radius (e.g., [1]), formally selfdual codes (e.g., [4]), additive codes (e.g., [5]), and decoding (e.g., [7]).
Teaching both research specialists and aspiring coding theory students was important to Vera. In 1982, she published her first coding theory book Introduction to the Theory of Error Correcting Codes [19], currently in its third edition, which provided a gentle introduction to the field. In 1992 Vera began work as coeditor of the two volume Handbook of Coding Theory [20]. This 25 chapter, 33 author Handbook, which covered a wide range of topics on the frontiers of research, was published six years after the project began. Upon its completion, the coeditors decided it would be appropriate to coauthor an extensive textbook that could provide in part a bridge to the Handbook. The result was Fundamentals of Error Correcting Codes [6] published in 2003.
During the mid 1980s Vera served on the Board of Governors of the Information Theory Society. In 2012 she became a fellow of the American Mathematical Society. During her career she published over 120 journal articles, 21 appearing in IEEE Transactions on Information Theory.
Vera is survived by her three children Naomi, Daniel, and Ben along with four grandchildren Lilah, Evie, Rebecca, and Jesse.
On a personal note, I had the privilege of working with Vera for over 30 years as our universities were only a subway ride (with one transfer) apart. Vera was always inspirational with her wealth of knowledge and intuitive insight into coding problems. In a very informal way, she taught me much coding theory as we sat in her office, probably not realizing how inﬂuential these conversations were. Vera loved classical music and reading; she loved her children and grandchildren. And she loved her students. On my visits, we would often go to lunch, usually at Vera’s favorite Thai restaurant, inviting one or two students; you could never move fast enough as she would quickly pick up the check. I served on the Ph.D. committees of a number of her students. When members would ask the student a question, Vera could barely restrain herself (and often did not) from answering for them – she so much wanted her students to succeed. In the days following her passing, I received emails from coding theorists whose research careers were nudged, and even redirected, along new paths based on interactions with Vera. Her presence will be greatly missed.
References

E. F. Assmus, Jr. and V. S. Pless. On the covering radius of extremal selfdual codes. IEEE Trans. Inform. Theory, 29:359–363, 1983.

E. R. Berlekamp, editor. Key Papers in the Development of Coding Theory. IEEE Press, New York, 1974.

I. F. Blake, editor. Algebraic Coding Theory History and Development. Hutchinson, & Ross, Inc. Stroudsburg, PA, USA, 1973. Dowden,

R. A. Brualdi and V. S. Pless. Greedy codes. J. Combin. Theory Ser. A, 64:10–30, 1993.

J. H. Conway, V. S. Pless, and N. J. A. Sloane. Selfdual codes over GF(3) and GF(4) of length not exceeding 16. IEEE Trans. Inform. Theory, 25:312–322, 1979.

J. E. Fields, P. Gaborit, W. C. Huffman, and V. S. Pless. On the classiﬁcation of extremal even formally selfdual codes of lengths 20 and 22. Discrete Appl. Math., 111:75–86, 2001.

P. Gaborit, W. C. Huffman, J.L. Kim, and V. S. Pless. On additive GF(4) codes. In Codes and Association Schemes (Piscataway, NJ, 1999), volume 56 of DIMACS Ser. Discrete Math. Theoret. Comput. Sci., pages 135–149. Amer. Math. Soc., Providence, RI, 2001.

W. C. Huffman and V. S. Pless. Fundamentals of ErrorCorrecting Codes. Cambridge University Press, Cambridge, 2003.

J.L. Kim and V. S. Pless. Decoding some doublyeven selfdual [32, 16, 8] codes by hand. In Codes and Designs (Columbus, OH, 2000), volume 10 of Ohio State Univ. Math. Res. Inst. Publ., pages 165–178. de Gruyter, Berlin, 2002.

J. S. Leon, J. M. Masley, and V. S. Pless. Duadic codes. IEEE Trans. Inform. Theory, 30:709–714, 1984.

F. J. MacWilliams. A theorem on the distribution of weights in a systematic code. Bell System Tech. J., 42:79–94, 1963.

V. S. Pless. Quotient Rings of Continuous Transformation Rings. PhD thesis, Northwestern University, 1957; available at ProQuest LLC, Ann Arbor, MI.

V. S. Pless. The continuous transformation ring of biorthogonal bases spaces. Duke Math. J., 25:365–371, 1958.

V. S. Pless. Power moment identities on weight distributions in error correcting codes. Inform. and Control, 6:147–152, 1963.

V. S. Pless. The number of isotropic subspaces in a ﬁnite geometry. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8), 39:418–421, 1965.

V. S. Pless. On the uniqueness of the Golay codes. J. Combin. Theory, 5:215–228, 1968.

V. S. Pless. A classiﬁcation of selforthogonal codes over GF(2). Discrete Math., 3:209246, 1972.

V. S. Pless. Symmetry codes over GF(3) and new ﬁvedesigns. J. Combin. Theory Ser. A, 12:119–142, 1972.

V. S. Pless. CAMAC—Combinatorial and Algebraic Machine Aided Computation. In Proceedings of the Sixth Southeastern Conference on Combinatorics, Graph Theory, and Computing (Florida Atlantic Univ., Boca Raton, Fla., 1975), pages 505–511. Congressus Numerantium, No,. XIV, 1975.

V. S. Pless. Qcodes. J. Combin. Theory Ser. A, 43:258–276, 1986.

V. S. Pless. Introduction to the Theory of ErrorCorrecting Codes. WileyInterscience Series in Discrete Mathematics and Optimization. John Wiley & Sons, Inc., New York, 3 rd edition, 1998.

V. S. Pless and W. C. Huffman, editors. Handbook of Coding Theory, Vol. I, II. NorthHolland, Amsterdam, 1998.

V. S. Pless and Z. Qian. Cyclic codes and quadratic residue codes over Z
_{
4
}
. IEEE Trans. Inform. Theory, 42:1594–1600, 1996.
 V. S. Pless, P. Solé, and Z. Qian. Cyclic selfdual Z _{ 4 } codes. Finite Fields Appl., 3:48–69, 1997.