2017/11/01 by Alexander M. Romanov, Romanov, Alexander M.
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Finite Group Theory Research #cs.DM #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1711.00189
arxiv created 2017/11/01 · openalex publication_date 2017/11/01 · arxiv updated 2017/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider perfect 1-error correcting codes over a finite field with q elements (briefly q-ary 1-perfect codes). In this paper, a generalized concatenation construction for q-ary 1-perfect codes is presented that allows us to construct q-ary 1-perfect codes of length (q - 1)nm + n + m from the given q-ary 1-perfect codes of length n =(qs1 - 1) / (q - 1) and m = (qs2 - 1) / (q - 1), where s1, s2 are natural numbers not less than two. This construction allows us to also construct q-ary codes with parameters (qs1 + s2, q^qs1 + s2 - (s1 + s2) - 1, 3)q and can be regarded as a q-ary analogue of the well-known Phelps construction.