On the covering radius of cyclic linear codes and arithmetic codes
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.
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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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Designing a good error-correcting code is a packing problem. The corresponding covering problem has received much less attention: now the codewords must be placed so that no vector of the space is very far from the nearest codeword. The two problems are quite different, and with a few exceptions good packings, i.e. codes with a large minimal distance, are usually not especially good coverings. ...
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On the way of generalizing recent results by Cock and the second author, it is shown that when the basis q is odd, BCH codes can be lengthened to obtain new codes with covering radius R = 2. These constructions (together with a lengthening construction by the first author) give new infinite families of linear covering codes with codimension r = 2k + 1 (the case q = 3, r = 4k + 1 was considered ...
متن کاملNew Bounds for Linear Codes of Covering Radius 2
The length function lq(r,R) is the smallest length of a q-ary linear code of covering radius R and codimension r. New upper bounds on lq(r, 2) are obtained for odd r ≥ 3. In particular, using the one-to-one correspondence between linear codes of covering radius 2 and saturating sets in the projective planes over finite fields, we prove that
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1985
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(85)80006-8