Self-dual codes over GF(q) with symmetric generator matrices

09/14/2020

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by   Whan-Hyuk Choi, et al.

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We introduce a consistent and efficient method to construct self-dual codes over GF(q) with symmetric generator matrices from a self-dual code over GF(q) of smaller length where q ≡ 1 4. Using this method, we improve the best-known minimum weights of self-dual codes, which have not significantly improved for almost two decades. We focus on a class of self-dual codes, including double circulant codes. Using our method, called a `symmetric building-up' construction, we obtain many new self-dual codes over GF(13) and GF(17) and improve the bounds of best-known minimum weights of self-dual codes of lengths up to 40. Besides, we compute the minimum weights of quadratic residue codes that were not known before. These are: a [20,10,10] QR self-dual code over GF(23), two [24,12,12] QR self-dual codes over GF(29) and GF(41), and a [32,12,14] QR self-dual codes over GF(19). They have the highest minimum weights so far.