Optimal ternary quasi-cyclic codes
Designs, Codes and Cryptography
New Minimum Distance Bounds for Linear Codes over Small Fields
Problems of Information Transmission
New One-Generator Quasi-cyclic Codes over GF(7)
Problems of Information Transmission
Optimal linear codes from matrix groups
IEEE Transactions on Information Theory
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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.