Abstract
The purpose of this paper is to improve the upper bounds of the minimum distances of self-dual codes over \({\mathbb{F}}_5\) for lengths [22, 26, 28, 32–40]. In particular, we prove that there is no [22, 11, 9] self-dual code over \({\mathbb{F}}_5\) , whose existence was left open in 1982. We also show that both the Hamming weight enumerator and the Lee weight enumerator of a putative [24, 12, 10] self-dual code over \({\mathbb{F}}_5\) are unique. Using the building-up construction, we show that there are exactly nine inequivalent optimal self-dual [18, 9, 7] codes over \({\mathbb{F}}_5\) up to the monomial equivalence, and construct one new optimal self-dual [20, 10, 8] code over \({\mathbb{F}}_5\) and at least 40 new inequivalent optimal self-dual [22, 11, 8] codes.
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Communicated by R. Hill.
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Han, S., Kim, JL. On self-dual codes over \({\mathbb{F}}_5\) . Des. Codes Cryptogr. 48, 43–58 (2008). https://doi.org/10.1007/s10623-008-9197-3
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DOI: https://doi.org/10.1007/s10623-008-9197-3