Information sets in quadratic-residue codes
نویسندگان
چکیده
منابع مشابه
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Generalized quadratic residue codes
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A long standing problem has been to develop “good” binary linear block codes, C, to be used for error-correction. The length of the block is denoted n and the dimension of the code is denoted k. So in this notation C ⊆ GF (2) is a k-dimensional subspace. Another important parameter is the smallest weight of any non-zero codeword, d. This is related to error-correction because C can correct [d−1...
متن کاملQuadratic Residue Codes and Divisibility
Quadratic residue codes are some of the brightest gems of coding theory. Their facets reeect many topics: quadratic residues and reciprocity; multiply transitive and sporadic simple groups; lattices; group representations; and block designs and Hadamard matrices. They provide the only perfect codes for prime-power sized alphabets correcting more than one error, and some are prototypes of extrem...
متن کاملQuadratic Residue Codes over Z 9
A subset of n tuples of elements of Z9 is said to be a code over Z9 if it is a Z9-module. In this paper we consider an special family of cyclic codes over Z9, namely quadratic residue codes. We define these codes in term of their idempotent generators and show that these codes also have many good properties which are analogous in many respects to properties of quadratic residue codes over finit...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1982
ISSN: 0012-365X
DOI: 10.1016/0012-365x(82)90222-9