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Orbit and coset analysis of the Golay and related codes

1990/01/01 by J.H. Conway, John H. Conway, N. J. A. Sloane +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Wireless Communication Techniques #Algorithm #Binary Golay code #Coding theory and cryptography #Computer science #Coset #Discrete mathematics #Mathematics #graph theory and CDMA systems

paper · doi:10.1109/18.57203

openalex publication_date 1990/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

Let b be a code of length n over a field F, with automorphism group G; b/sub w/ denotes the subset of codewords of weight w. The goal is to classify the vectors of F/sup n/ into orbits under G and to determine their distances from the various subcodes b/sub w/. This is done for the first-order Reed-Muller, Nordstrom-Robinson, and Hamming codes of length 16, the Golay and shortened Golay codes of lengths 22, 23, 24, and the ternary Golay code of length 12.>

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