TY - JOUR
T1 - Completely regular codes with different parameters giving the same distance-regular coset graphs
AU - Rifà, J.
AU - Zinoviev, V. A.
PY - 2017/7/1
Y1 - 2017/7/1
N2 - © 2017 Elsevier B.V. We construct several classes of completely regular codes with different parameters, but identical intersection array. Given a prime power q and any two natural numbers a,b, we construct completely transitive codes over different fields with covering radius ρ=min{a,b} and identical intersection array, specifically, one code over Fqr for each divisor r of a or b. As a corollary, for any prime power q, we show that distance regular bilinear forms graphs can be obtained as coset graphs from several completely regular codes with different parameters.
AB - © 2017 Elsevier B.V. We construct several classes of completely regular codes with different parameters, but identical intersection array. Given a prime power q and any two natural numbers a,b, we construct completely transitive codes over different fields with covering radius ρ=min{a,b} and identical intersection array, specifically, one code over Fqr for each divisor r of a or b. As a corollary, for any prime power q, we show that distance regular bilinear forms graphs can be obtained as coset graphs from several completely regular codes with different parameters.
KW - Bilinear forms graph
KW - Completely regular code
KW - Completely transitive code
KW - Coset graph
KW - Distance-regular graph
KW - Distance-transitive graph
KW - Kronecker product construction
KW - Lifting of a field
KW - Uniformly packed code
U2 - 10.1016/j.disc.2017.03.001
DO - 10.1016/j.disc.2017.03.001
M3 - Article
SN - 0012-365X
VL - 340
SP - 1649
EP - 1656
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 7
ER -