THE EQUIVALENT IDENTITIES OF THE MACWILLIAMS IDENTITIES FOR LINEAR CODES

Authors

  • Bao Xiaomin School of Mathematics & Statistics, Southwest University, Chongqing, 400715, China

DOI:

https://doi.org/10.11113/jt.v76.4035

Keywords:

Linear code, Hamming weight, MacWilliams identity, equivalent, derivative

Abstract

We use derivatives to prove the equivalences between MacWilliams identity and its four equivalent forms, and present new interpretations for the four equivalent forms.

References

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Brualdi R. A., V. S. Pless and J. Beissinger. 1988. On the MacWilliams Identities for Linear Codes. Linear Algebra Appl. 107: 181-189.

Chang, S. C. and J. K. Wolf. 1980. A Simple Derivation of the MacWilliams' Identity for Linear Codes. IEEE Tran. On Inform. Theory. IT-26(4): 476-477.

Goldwasser, J. L. 1997. Shortened and Punctured Codes and the MacWilliams Identities. Linear Algebra Appl. 253: 1-13.

Honold, T. 1996. A Proof of MacWilliams' Identity. J. of Geometry. 57: 120-122.

MacWilliams, F. J. 1963. A Theorem on the Distribution of Weights in a Systematic Code. Bell System Tech. J. 42: 79-94.

MacWilliams, F. J. and N. J. A. Sloane. 1977. The Theory of Error-Correcting Codes. New York: North-Holland Publishing Company.

Pless, V. S. 1989. Introduction to the Theory of Error-Correcting Codes. 2nd ed. New York:Wiley-Interscience.

Zierler, N. 1973. On the MacWilliams Identity. J. Combinatorial Theory (A). 15: 333-337.

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Published

2015-08-30

Issue

Section

Science and Engineering

How to Cite

THE EQUIVALENT IDENTITIES OF THE MACWILLIAMS IDENTITIES FOR LINEAR CODES. (2015). Jurnal Teknologi, 76(1). https://doi.org/10.11113/jt.v76.4035