On a class of repeated-root monomial-like abelian codes | Zendy

Edgar Martı́nez-Moro | Zendy; Hakan Özadam | Zendy; Ferruh Özbudak | Zendy; Steve Szabo | Zendy

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On a class of repeated-root monomial-like abelian codes

Author(s) -

Edgar Martı́nez-Moro,

Hakan Özadam,

Ferruh Özbudak,

Steve Szabo

Publication year - 2015

Publication title -

journal of algebra combinatorics discrete structures and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.137

H-Index - 1

ISSN - 2148-838X

DOI - 10.13069/jacodesmath.17537

Subject(s) - monomial , abelian group , class (philosophy) , mathematics , root (linguistics) , combinatorics , discrete mathematics , pure mathematics , computer science , artificial intelligence , linguistics , philosophy

In this paper we study polycyclic codes of length $p^{s_1} \times \cdots \times p^{s_n}$\ over $\F_{p^a}$\ generated by a single monomial. These codes form a special class of abelian codes. We show that these codes arise from the product of certain single variable codes and we determine their minimum Hamming distance. Finally we extend the results of Massey et. al. in \cite{MASSEY_1973} on the weight retaining property of monomials in one variable to the weight retaining property of monomials in several variables.

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