Abstract
We present a family of reducible cyclic codes constructed as a direct sum (as vector spaces) of two different semiprimitive two-weight irreducible cyclic codes. This family generalizes the class of reducible cyclic codes that was reported in the main result of [10]. Moreover, despite of what was stated therein, we show that, at least for the codes studied here, it is still possible to compute the frequencies of their weight distributions through the cyclotomic numbers in an easy way.
Highlights
It is said that a cyclic code is reducible if its parity-check polynomial is factorizable in two or more irreducible factors
We present a family of reducible cyclic codes constructed as a direct sum of two different semiprimitive two-weight irreducible cyclic codes
Despite of what was stated therein, we show that, at least for the codes studied here, it is still possible to compute the frequencies of their weight distributions through the cyclotomic numbers in an easy way
Summary
It is said that a cyclic code is reducible if its parity-check polynomial is factorizable in two or more irreducible factors. At, let C(a1,a2,a3,...,at) be the cyclic code with parity-check polynomial t i=1 hai (x) With this notation, the following result gives a description for the weight distribution of a family of reducible cyclic codes: Theorem. In [8] was given a unified explanation for the weight distribution of several families of codes whose parity-check polynomials are given by the products of the form ha (x)h a±. From this perspective, it is important to keep in mind that the paritycheck polynomials of the kind of codes studied in [10], and those studied by Theorem 1.1, are given by the products of the form ha. The following result is on that direction ([5])
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Journal of Algebra Combinatorics Discrete Structures and Applications
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
