Nonexistence of some ternary linear codes

We prove the nonexistence of some ternary linear codes of dimension 6, which implies that n3(6,d)=g3(6,d)+2 for d=48,49,66,67,149,150, where g3(k,d)=∑i=0k−1⌈d/3i⌉ and nq(k,d) denotes the minimum length n for which an [n,k,d]q code exists. To prove the nonexistence of a putative code through projecti...

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Bibliographic Details
Published in:Discrete mathematics 2021-11, Vol.344 (11), p.112572, Article 112572
Main Authors: Sawashima, Toshiharu, Maruta, Tatsuya
Format: Article
Language:English
Subjects:
Optimal codes
Projective geometry
Ternary linear codes
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Summary:We prove the nonexistence of some ternary linear codes of dimension 6, which implies that n3(6,d)=g3(6,d)+2 for d=48,49,66,67,149,150, where g3(k,d)=∑i=0k−1⌈d/3i⌉ and nq(k,d) denotes the minimum length n for which an [n,k,d]q code exists. To prove the nonexistence of a putative code through projective geometry, we introduce some proof techniques such as i-Max and i-Max-NS to rule out some possible weights of codewords.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2021.112572