The b-symbol weight distributions of all semiprimitive irreducible cyclic codes
Gerardo Vega
TL;DR
This paper generalizes and simplifies the determination of the b-symbol weight distributions for all one-weight and two-weight semiprimitive irreducible cyclic codes, extending previous specific cases.
Contribution
It provides a unified approach to compute the b-symbol weight distributions for all such codes, broadening the scope of prior results.
Findings
Complete b-symbol weight distributions for all one-weight codes
Complete b-symbol weight distributions for all two-weight codes
Simplified formulas applicable to a wide class of codes
Abstract
Up to a new invariant , the complete -symbol weight distribution of a particular kind of two-weight irreducible cyclic codes, was recently obtained by Zhu et al. [Des. Codes Cryptogr., 90 (2022) 1113-1125]. The purpose of this paper is to simplify and generalize the results of Zhu et al., and obtain the -symbol weight distributions of all one-weight and two-weight semiprimitive irreducible cyclic codes.
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Taxonomy
TopicsCoding theory and cryptography · Islamic Finance and Communication · Pancasila Values in Education