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A new family of binary linear completely transitive (and, therefore, completely regular) codes is constructed. The covering radius of these codes is growing with the length of the code. In particular, for any integer r > 1, there exist two codes with d=3, covering radius r and length 2r(4r-1) and (2r+1)(4r+1), respectively. These new completely transitive codes induce, as coset graphs, a family of distance-transitive graphs of growing diameter.
Completely regular codes with covering radius $rho=1$ must have minimum distance $dleq 3$. For $d=3$, such codes are perfect and their parameters are well known. In this paper, the cases $d=1$ and $d=2$ are studied and completely characterized when t
Given a parity-check matrix $H_m$ of a $q$-ary Hamming code, we consider a partition of the columns into two subsets. Then, we consider the two codes that have these submatrices as parity-check matrices. We say that anyone of these two codes is the s
The list-decodable code has been an active topic in theoretical computer science since the seminal papers of M. Sudan and V. Guruswami in 1997-1998. There are general result about the Johnson radius and the list-decoding capacity theorem for random c
In this paper new infinite families of linear binary completely transitive codes are presented. They have covering radius $rho = 3$ and 4, and are a half part of the binary Hamming and the binary extended Hamming code of length $n=2^m-1$ and $2^m$, r
We investigate the asymptotic rates of length-$n$ binary codes with VC-dimension at most $dn$ and minimum distance at least $delta n$. Two upper bounds are obtained, one as a simple corollary of a result by Haussler and the other via a shortening app