Open AccessOn the algebraic structure of polycyclic codes
Author(s) -
Hassan Ou-Azzou,
Mustapha Najmeddine
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2110407o
Subject(s) - mathematics , linear subspace , cyclic code , invariant (physics) , dual code , discrete mathematics , hamming code , code (set theory) , algebraic number , polynomial ring , polynomial code , bch code , combinatorics , polynomial , linear code , pure mathematics , algorithm , error detection and correction , computer science , block code , mathematical analysis , decoding methods , set (abstract data type) , mathematical physics , programming language
In this paper, we are interested in the study of the right polycyclic codes as invariant subspaces of Fnq by a fixed operator TR. This approach has helped in one hand to connect them to the ideals of the polynomials ring Fq [x]/?f)X)?, where f (x) is the minimal polynomial of TR. On the other hand, it allows to prove that the dual of a right polycyclic code is invariant by the adjoint operator of TR. Hence, when TR is normal we prove that the dual code of a right polycyclic code is also a right polycyclic code. However, when TR isn?t normal the dual code is equivalent to a right polycyclic code. Finally, as in the cyclic case, the BCH-like and Hartmann-Tzeng-like bounds for the right polycyclic codes on Hamming distance are derived.