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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 the codes are linear. Moreover, it is proven that all these codes are completely transitive.
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
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
This work is a survey on completely regular codes. Known properties, relations with other combinatorial structures and constructions are stated. The existence problem is also discussed and known results for some particular cases are established. In p
New quaternary Plotkin constructions are given and are used to obtain new families of quaternary codes. The parameters of the obtained codes, such as the length, the dimension and the minimum distance are studied. Using these constructions new famili
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