MACWILLIAMS IDENTITIES

MACWILLIAMS, JESSIE.

A Theorem on the Distribution of Weights in a Systematic Code.

New York, American Telephone and Telegraph Company, 1963. 8vo. Volume XLII, January, Number 1, 1963 of "The Bell System Technical Journal". In the original printed blue wrapper. Previous owner's stamp to front wrapper. Spine slightly discoulered and lower right corner slightly bumped. A nice and clean copy. Pp. 79-94. [Entire issue: 206 pp].

First publication of MacWilliams Identities, or the MacWilliams Equation, which became the starting point for a considerable amount of research in coding theory and cryptology by the Bell System. MacWilliams Identities are essentially a set of linear relations of weight distribution which specifies the number of words of each possible Hamming weight. The development of the MacWilliams Identities had profound influence in practical as well as theoretical cryptology.

"Another major theoretical advance was F. J. MacWilliams's discovery in the 1962 [the present paper, published in January 1963] of a set of fundamental equations [now called the MacWilliams Identities] that any linear code must satisfy. These identities were the starting point for a considerable amount of research by MacWilliams, C. L. Mallows, N. J. A. Sloane, and others". (Millman, A History of Engineering & Science in the Bell System, 1984, p. 54).

"MacWilliams (1917-1990) was a mathematician who contributed to the field of coding theory. She was born in Stoke-on-Trent, England and studied at the University of Cambridge, receiving her BA in 1938 and her MA in the following year. She spent most of her career at Bell Labs, where she worked on error-correcting codes and co-wrote The Theory of Error-Correcting Code with Neil Sloane." (Codings: Webster's Quotations, 42 p.)

The issue contains the following papers:
1. Beach, C.D.; Trecker, J.M. A Method for Predicting Interchannel Modulation due to Multipath Propagation in FM and PM Tropospheric Radio Systems. Pp. 1-36.
2. Bodtmann, W.F.; Ruthroff, C.L. A Wideband Transistor IF Amplifier for Space and Terrestrial Repeaters Using Grounded-Base Transformer-Coupled Stages. Pp. 37-54.
3. Coyne, J.C. Monitoring the Percussive Welding Process for Attaching Wires to Terminals. Pp. 55-78.
4. MacWilliams, Jessie. A Theorem on the Distribution of Weights in a Systematic Code. Pp. 79-94.
5. Peck, D.S.; Blair, R.R.; Brown, W.L.; Smits, F.M. Surface Effects of Radiation on Transistors. Pp. 95-129.
6. Graff, H.J.; Peacock, J.M.; Zalmans, J.J. Development of Solderless Wire Connector for Splicing Multipair Cable. Pp. 131-153.
7. Gordon, E.I.; Rigden, J.D. The Fabry-Perot Electrooptic Modulator. Pp. 155-179.
8. Pfahnl, Arnold. Properties of Fast-Decay Cathode-Ray Tube Phosphors. Pp. 181-201.

Order-nr.: 43549