Generalized hypercube graph $\Q_n(S)$, graph products and self-orthogonal codes

Journal of Algebra Combinatorics Discrete Structures and Applications

article

Pani Seneviratne¹ 

[1] Texas A&M University-Commerce

关键词: Graphs;    Designs;    Codes;    Permutation decoding;   

DOI  :  10.13069/jacodesmath.13099

学科分类：社会科学、人文和艺术（综合）

来源: Yildiz Technical University

【 摘 要 】

A generalized hypercube graph Qn(S) has Fn2 = {0, 1}nas the vertex set and two vertices beingadjacent whenever their mutual Hamming distance belongs to S, where n ≥ 1 and S ⊆ {1, 2, . . . , n}.The graph Qn({1}) is the n-cube, usually denoted by Qn. We study graph boolean products G1 =Qn(S) × Q1, G2 = Qn(S) ∧ Q1, G3 = Qn(S)[Q1] and show that binary codes from neighborhooddesigns of G1, G2 and G3 are self-orthogonal for all choices of n and S. More over, we show that theclass of codes C1 are self-dual. Further we find subgroups of the automorphism group of these graphsand use these subgroups to obtain PD-sets for permutation decoding. As an example we find a fullerror-correcting PD set for the binary [32, 16, 8] extremal self-dual code.

【 授权许可】

CC BY