Designs and their codes
Quadratic double circulant codes over fields
Journal of Combinatorial Theory Series A
Euclidean and hermitian self-dual MDS codes over large finite fields
Journal of Combinatorial Theory Series A
Skew Hadamard designs and their codes
Designs, Codes and Cryptography
Experimental constructions of self-dual codes
Finite Fields and Their Applications
There exists no self-dual [24,12,10] code over $${{\mathbb F}_5}$$
Designs, Codes and Cryptography
Self-dual Codes over Small Prime Fields from Combinatorial Designs
CAI '09 Proceedings of the 3rd International Conference on Algebraic Informatics
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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.