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Extendability of Ternary Linear Codes

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Abstract

There are four diversities for which ternary linear codes of dimension k ≥ 3, minimum distance d with gcd(3,d) = 1 are always extendable. Moreover, three of them yield double extendability when d ≡ 1 (mod 3). All the diversities are found for ternary linear codes of dimension 3 ≤ k ≤ 6. An algorithm how to find an extension from a generator matrix is also given.

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Authors and Affiliations

  1. Department of Applied Mathematics, Osaka Women’s University, Daisen-cho, Osaka, 590-0035, Japan

    Tatsuya Maruta

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  1. Tatsuya Maruta
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Correspondence to Tatsuya Maruta.

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This research has been partially supported by Grant-in-Aid for Scientific Research of the Ministry of Education under Contract Number 304-4508-12640137

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Maruta, T. Extendability of Ternary Linear Codes. Des Codes Crypt 35, 175–190 (2005). https://doi.org/10.1007/s10623-005-6400-7

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  • DOI: https://doi.org/10.1007/s10623-005-6400-7

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