A first step towards the skew duadic codes | Zendy

Delphine Boucher | Zendy

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A first step towards the skew duadic codes

Author(s) -

Delphine Boucher

Publication year - 2018

Publication title -

advances in mathematics of communications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.601

H-Index - 26

eISSN - 1930-5346

pISSN - 1930-5338

DOI - 10.3934/amc.2018033

Subject(s) - skew , automorphism , combinatorics , mathematics , enumeration , prime (order theory) , discrete mathematics , binary number , block code , dual (grammatical number) , binary code , computer science , arithmetic , algorithm , decoding methods , telecommunications , art , literature

This text gives a first definition of the $\theta$-duadic codes where $\theta$ is an automorphism of $F q$. A link with the weakly self-dual $\theta$-cyclic codes is established. A construction and an enumeration are provided when $q$ is the square of a prime number $p$. In addition, new self-dual binary codes $ [72, 36, 12] $ are obtained from extended $\theta$-duadic codes defined on $F 4$.

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