TY - JOUR
T1 - Families of nested completely regular codes and distance-regular graphs
AU - Borges, Joaquim
AU - Rifà, Josep
AU - Zinoviev, Victor A.
PY - 2015/1/1
Y1 - 2015/1/1
N2 - © 2015 AIMS. In this paper infinite families of linear binary nested completely regular codes are constructed. They have covering radius ∈ equal to 3 or 4; and are 1=2ith parts, for i ϵ {1,…,u} of binary (respectively, extended binary) Hamming codes of length n = 2m–1 (respectively, 2m), where m = 2u. In the usual way, i.e., as coset graphs, infinite families of embedded distance-regular coset graphs of diameter D equal to 3 or 4 are constructed. This gives antipodal covers of some distance-regular and distance-transitive graphs. In some cases, the constructed codes are also completely transitive and the corresponding coset graphs are distance-transitive.
AB - © 2015 AIMS. In this paper infinite families of linear binary nested completely regular codes are constructed. They have covering radius ∈ equal to 3 or 4; and are 1=2ith parts, for i ϵ {1,…,u} of binary (respectively, extended binary) Hamming codes of length n = 2m–1 (respectively, 2m), where m = 2u. In the usual way, i.e., as coset graphs, infinite families of embedded distance-regular coset graphs of diameter D equal to 3 or 4 are constructed. This gives antipodal covers of some distance-regular and distance-transitive graphs. In some cases, the constructed codes are also completely transitive and the corresponding coset graphs are distance-transitive.
KW - Completely regular codes
KW - Completely transitive codes
KW - Distance-regular graphs
KW - Distance-transitive graphs
UR - https://publons.com/publon/9675739/
U2 - 10.3934/amc.2015.9.233
DO - 10.3934/amc.2015.9.233
M3 - Article
SN - 1930-5346
VL - 9
SP - 233
EP - 246
JO - Advances in Mathematics of Communications
JF - Advances in Mathematics of Communications
ER -