A New [ 14 8 3 ]-Linear Code From the Aunu Generated [ 7 4 2 ] -Linear Code and the Known [7 4 3 ] Hamming Code Using the (U|U+V) Construction

Journal of Applied & Computational Mathematics

article

Ibrahim AA¹  Chun PB²  Kamoh NM³ 

[1] Department of Mathematics, Usmanu Danfodiyo University;Department of Mathematics, Plateau State University Bokkos;Department of Mathematics, Bingham University

关键词: Cayley tables;    AUNU scheme;    Hamming codes;    Standard generator matrix;    Extended code;    Reduced Row Echelon form (RREF);    [n k d] linear code;    (u|u+v) construction;    Parity check matrix;   

DOI  :  10.4172/2168-9679.1000379

来源: Hilaris Publisher

【 摘 要 】

In this communication, we enumerate the construction of a [ 7 4 2 ]- linear code which is an extended code of the [ 6 4 1 ] code and is in one-one correspondence with the known [ 7 4 3 ] - Hamming code. Our construction is due to the Carley table for n=7of the generated points of was permutations of the (132) and (123)-avoiding patterns of the non-associative AUNU schemes. Next, [ 7 4 2 ] linear code so constructed is combined with the known Hamming [ 7 4 3 ] code using the ( u|u+v)-construction to obtain a new hybrid and more practical single [14 8 3 ] error- correcting code.

【 授权许可】

Unknown