Abstract
This paper gives new methods of constructing symmetric self-dual codes over a finite field GF(q) where q is a power of an odd prime. These methods are motivated by the well-known Pless symmetry codes and quadratic double circulant codes. Using these methods, we construct an amount of symmetric self-dual codes over GF(11), GF(19), and GF(23) of every length less than 42. We also find 153 new self-dual codes up to equivalence: they are [32, 16, 12], [36, 18, 13], and [40, 20, 14] codes over GF(11), [36, 18, 14] and [40, 20, 15] codes over GF(19), and [32, 16, 12], [36, 18, 14], and [40, 20, 15] codes over GF(23). They all have new parameters with respect to self-dual codes. Consequently, we improve bounds on the highest minimum distance of self-dual codes, which have not been significantly updated for almost two decades.
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The authors sincerely thank Dr. Markus Grassl for his helpful comments which was crucial for the implementation.
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The author (Whan-Hyuk Choi) is supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea Government (NRF-2019R1I1A1A01057755) and is supported by NRF under the project code 2020K2A9A1A06108874. The author (Jon-Lark Kim) is supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (NRF-2019R1A2C1088676) and is supported by NRF under the project code 2020K2A9A1A06108874.
This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue: On Coding Theory and Combinatorics: In Memory of Vera Pless”.
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Choi, W.H., Kim, J.L. An improved upper bound on self-dual codes over finite fields GF(11), GF(19), and GF(23). Des. Codes Cryptogr. 90, 2735–2751 (2022). https://doi.org/10.1007/s10623-021-00968-3
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DOI: https://doi.org/10.1007/s10623-021-00968-3