Abstract
We construct new families of completely regular codes by concatenation methods. By combining parity check matrices of cyclic Hamming codes, we obtain families of completely regular codes. In all cases, we compute the intersection array of these codes. We also study when the extension of these codes gives completely regular codes. Some of these new codes are completely transitive.
Highlights
Let Fq be a finite field of the order q
A q-ary linear [n, k, d; ρ]q-code C is a k-dimensional subspace of Fnq, where n is the length, d is the minimum distance, qk is the cardinality of C, and ρ is the covering radius
Let C be a linear code over Fq with covering radius ρ
Summary
Let Fq be a finite field of the order q. A q-ary code C of length n and covering radius ρ is completely regular, if for all l ≥ 0 every vector x ∈ C(l) has the same number cl of neighbors in C(l − 1) and the same number bl of neighbors in C(l + 1). Acts on the set of cosets of C in the following way: for all π ∈ Aut(C) and for every vector v ∈ Fnq we have π(v + C) = π(v) + C. Let C be a linear code over Fq with covering radius ρ. C is completely transitive if Aut(C) has ρ + 1 orbits when acts on the cosets of C. Since two cosets in the same orbit have the same weight distribution, it is clear that any completely transitive code is completely regular. We extend these constructions, giving several explicit constructions of new completely regular and completely transitive codes, based on concatenation methods
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 callDisclaimer: 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.
