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Construction of a (64, 2 37, 12) Code via Galois Rings (1997)

Calderbank, A. R. ; McGuire, Gary

Springer

Designs, codes and cryptography 10 (1997), S. 157-165

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ISSN: 1573-7586

Keywords: Algebraic coding theory ; codes over rings

Source: Springer Online Journal Archives 1860-2000

Topics: Computer Science , Mathematics

Notes: Abstract Certain nonlinear binary codes contain more codewords than any comparable linear code presently known. These include the Kerdock and Preparata codes, which exist for all lengths 4m ≥ 16. At length 16 they coincide to give the Nordstrom-Robinson code. This paper constructs a nonlinear (64, 237, 12) code as the binary image, under the Gray map, of an extended cyclic code defined over the integers modulo 4 using Galois rings. The Nordstrom-Robinson code is defined in this same way, and like the Nordstrom-Robinson code, the new code is better than any linear code that is presently known.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1008240319733

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