Enumeration of Self-Dual Codes of Length 6 over ? p

Whan-Hyuk Choi
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Whan-Hyuk Choi: Department of Mathematics, 1 Gangwondaehakgil, Kangwon National University, Chuncheon 24341, Korea

Mathematics, 2019, vol. 7, issue 10, 1-16

Abstract: The purpose of this paper is to classify and enumerate self-dual codes of length 6 over finite field Z p . First, we classify these codes into three cases: decomposable, indecomposable non-MDS and MDS codes. Then, we complete the classification of non-MDS self-dual codes of length 6 over Z p for all primes p in terms of their automorphism group. We obtain all inequivalent classes and find the necessary and sufficient conditions for the existence of each class. Finally, we obtain the number of MDS self-dual codes of length 6.

Keywords: self-dual codes; MDS codes; classification; automorphism group; mass formula (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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