A new upper bound on nonbinary block codes
نویسندگان
چکیده
منابع مشابه
A New Class of Nonbinary Codes Meeting the Griesmer Bound
A new class of codes over GF(q’) that meet the Griesmer bound are constructed in a simple way from the Solomon and Stiffler codes over GF(q). The new codes are, in general, not equivalent to the Solomon and Stiffler codes whenever I > 1.
متن کاملУДК 53 B. Mounits NEW UPPER BOUNDS FOR NONBINARY CODES
New upper bounds on codes are presented. The bounds are obtained by linear and semidefinite programming. INTRODUCTION One of the central problems in coding theory is to find upper bounds on maximum size Aq(n, d) of a code of word length n and minimum Hamming distance at least d over the alphabet Q of q ≥ 2 letters. Let us provide Q with the structure of an Abelian group, in an arbitrary way. In...
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For nonbinary codes it is proved that the Hamming bound is asymptotically sharp in some range of the code rate.
متن کاملNew upper bounds for nonbinary codes based on the Terwilliger algebra and semidefinite programming
We give a new upper bound on the maximum size Aq(n, d) of a code of word length n and minimum Hamming distance at least d over the alphabet of q ≥ 3 letters. By blockdiagonalizing the Terwilliger algebra of the nonbinary Hamming scheme, the bound can be calculated in time polynomial in n using semidefinite programming. For q = 3, 4, 5 this gives several improved upper bounds for concrete values...
متن کاملA New Upper Bound for the Dimension of Trace Codes
We shall derive a new non-trivial upper bound for the dimension of trace codes connected to algebraicgeometric codes. Furthermore, we shall deduce their true dimension if certain conditions are satisfied.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1990
ISSN: 0012-365X
DOI: 10.1016/0012-365x(90)90002-y