All binary codes with covering radius one are subnormal
نویسندگان
چکیده
منابع مشابه
On the covering radius of some binary cyclic codes
We compute the covering radius of some families of binary cyclic codes. In particular, we compute the covering radius of cyclic codes with two zeros and minimum distance greater than 3. We compute the covering radius of some binary primitive BCH codes over F2f , where f = 7, 8.
متن کاملLinear codes with covering radius 3
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.
متن کاملAsymmetric Binary Covering Codes
An asymmetric binary covering code of length n and radius R is a subset C of the n-cube Qn such that every vector x ∈ Qn can be obtained from some vector c ∈ C by changing at most R 1’s of c to 0’s, where R is as small as possible. K(n,R) is defined as the smallest size of such a code. We show K(n,R) ∈ Θ(2/n) for constant R, using an asymmetric sphere-covering bound and probabilistic methods. W...
متن کاملOn 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.
متن کاملOn a family of binary completely transitive codes with growing covering radius
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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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1991
ISSN: 0012-365X
DOI: 10.1016/0012-365x(91)90028-z