On a class of binary linear completely transitive codes with arbitrary covering radius
نویسندگان
چکیده
منابع مشابه
On binary linear completely regular and completely transitive codes with arbitrary covering radius
An infinite class of binary linear completely regular and completely transitive codes is given. The covering radius of these codes is growing with the length of the code.
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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 ρ ≥ 2, there exist two codes with d = 3, covering radius ρ and length ( 4 ρ 2 )
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Completely regular codes with covering radius ρ = 1 must have minimum distance d ≤ 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.
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The shortest possible length of a q-ary linear code of covering radius R and codimension r is called the length function and is denoted by q(r, R). Constructions of codes with covering radius 3 are here developed, which improve best known upper bounds on q(r, 3). General constructions are given and upper bounds on q(r, 3) for q = 3, 4, 5, 7 and r ≤ 24 are tabulated.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2009
ISSN: 0012-365X
DOI: 10.1016/j.disc.2009.03.004