Abstract
Let [n, k, d] q -codes be linear codes of length n, dimension k, and minimum Hamming distance d over GF(q). In this paper we consider codes over GF(3), GF(5), GF(7), and GF(8). Over GF(3), three new linear codes are constructed. Over GF(5), eight new linear codes are constructed and the nonexistence of six codes is proved. Over GF(7), the existence of 33 new codes is proved. Over GF(8), the existence of ten new codes and the nonexistence of six codes is proved. All of these results improve the corresponding lower and upper bounds in Brouwer's table [www.win.tue.nl/∼aeb/voorlincod.html].
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Daskalov, R.N., Gulliver, T.A. New Minimum Distance Bounds for Linear Codes over Small Fields. Problems of Information Transmission 37, 206–215 (2001). https://doi.org/10.1023/A:1013873906597
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DOI: https://doi.org/10.1023/A:1013873906597