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G. Feng, Xinwen Wu, T. Rao (1997)
New double-byte error-correcting codes for memory systemsProceedings of IEEE International Symposium on Information Theory
J.H. Lint, G. Geer (1990)
Introduction to Coding Theory and Algebraic Geometry. DMV Seminar, Vol. 12
J.H. Lint (1988)
Coding Theory and Design Theory, Vol. 20 (IMA Volumes in Mathematics and Its Application)
V. Goppa (1988)
Geometry and Codes
(1980)
Algebra and Coding theory
$ : Algorithm to decide the minimum distance
M.A. Tsfasman, S.G. Vlâdut (1991)
Algebraic-Geometric Codes. In: Mathematics and Its Applications, Vol.58
R. Gallager, W. Peterson (1962)
Error-Correcting CodesScientific American
Output : $D_{p}(n, k)$ and the number of corresponding GCCs
O. Antoine, Berthet
Theory of Error-correcting Codes
M. Tsfasman, S. Vladut (1991)
Algebraic-Geometric Codes
Step 1) Construct a generating matrix $G_{k,n}$ from $g(x)$
V.D. Goppa (1991)
Mathematics and Its Application, Vol. 24
Step $3$ ) $[\mathrm{d}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{d}]d=D(n, k
F. MacWilliams, N. Sloane (1977)
The Theory of Error-Correcting Codes
2 Searching Algorithm for GCC. Input : $n,$ $k
E. Prange (1962)
The use of information sets in decoding cyclic codesIRE Trans. Inf. Theory, 8
Step 2) By seeing all possible codewords to decide $d$
J. Lint, G. Geer (1989)
Introduction to coding theory and algebraic geometry
Output : $\mathrm{d}$ , the minimum distance for a given GCC generated by $g(x)$
In this paper, we discuss how to construct a class of generalized cyclic codes, denoted by GCC. It is well known that a cyclic code is generated by a factor ofx n-1. Clearly, any monic polynomialg(x) with degree less thann could be considered as a factor of some polynomial of degreen. Similarly the construction of cyclic codes, we explain howg(x) can generate a GCC. Meanwhile, as related to cyclic codes, experiments show that GCC can always produce a better parameter and/or give more linear codes. On the basis the of concept of GCC, we can also construct a linear code of [90,76,5]2.
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Jul 7, 2007
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