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Some high-rate linear codes over GF(5) and GF(7)

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Abstract

Let an [n, k, d] q code be a linear code of length n, dimension k, and with minimum Hamming distance d over GF(q). The ratio R = k/n is called the rate of a code. In this paper, [62, 53, 6]5, [62, 48, 8]5, [71, 56, 8]5, [124, 113, 6]5, [43, 36, 6]7, [33, 23, 7]7, and [27, 18, 7]7 high-rate codes and new codes with parameters [42, 14, 19]5, [42, 15, 18]5, [48, 13, 24]5, [52, 12, 28]5, [71, 15, 38]5, [71, 16, 36]5, [72, 12, 41]5, [78, 10, 50]5, [88, 11, 54]5, [88, 13, 51]5, [124, 14, 77]5, [32, 12, 15]7, [32, 10, 17]7, [36, 10, 20]7, and [48, 10, 29]7 are constructed. The codes with parameters [62, 53, 6]5 and [43, 36, 6]7 are optimal.

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Authors and Affiliations

  1. Department of Mathematics, Technical University of Gabrovo, Bulgaria

    R. Daskalov

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  1. R. Daskalov
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Original Russian Text © R. Daskalov, 2007, published in Problemy Peredachi Informatsii, 2007, Vol. 43, No. 2, pp. 65–73.

Supported in part by the Bulgarian Ministry of Education and Science under Contract in TU-Gabrovo.

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Daskalov, R. Some high-rate linear codes over GF(5) and GF(7). Probl Inf Transm 43, 124–131 (2007). https://doi.org/10.1134/S0032946007020056

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  • DOI: https://doi.org/10.1134/S0032946007020056

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