On linear codes whose weights and length have a common divisor
نویسندگان
چکیده
منابع مشابه
On linear codes whose weights and length have a common divisor
Certain problems in coding theory translate naturally into problems concerning point sets in projective or affine space with special intersection properties with respect to certain subspaces. As an example, consider a set of p points in AG(3, p) which intersects every plane in 0 mod p points. Must this set necessarily be the union of p parallel lines? In the talk a very much related problem wil...
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Let F be a finite field with q elements. A k dimensional subspace C of the vector space Fn of all n-tuples over F is called a linear code of length n and dimension k. Algebraically, C is just a k-dimensional vector space over F. However, as a particular subspace of Fn, C inherits some metric properties. Specifically, for every v E Fn, the weight of v, denoted by wt( v), is defined to be the num...
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A recent paper described a variable-length integer code based on the Goldbach conjecture where every codeword had exactly 2 1-bits but with an extremely irregular structure. A later, unpublished, work produced a much more regular code, again with a Hamming weight of 2. This paper extends that later work to weight-3 and weight-4 codes, which are shown to be competitive with more-usual codes over...
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چکیده ندارد.
15 صفحه اولA class of cyclic codes whose duals have five zeros
In this paper, a family of cyclic codes over Fp whose duals have five zeros is presented, where p is an odd prime. Furthermore, the weight distributions of these cyclic codes are determined.
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2007
ISSN: 0001-8708
DOI: 10.1016/j.aim.2006.07.011