2015/10/23 by Josep Rifà, Rifà, J., Victor Zinoviev +1
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1510.06903
openalex publication_date 2015/10/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
A known Kronecker construction of completely regular codes has been investigated taking different alphabets in the component codes. This approach is also connected with lifting constructions of completely regular codes. We obtain 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. Under the same conditions, an explicit construction of an infinite family of q-ary uniformly packed codes (in the wide sense) with covering radius ρ, which are not completely regular, is also given.