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Massey’s Theorem and the Golay Codes

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Communications and Cryptography

Part of the book series: The Springer International Series in Engineering and Computer Science ((SECS,volume 276))

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Abstract

Massey’s theorem is used to determine the minimum distance of the Golay codes. The same method can be used to determine the minimum distance of other cyclic codes. This suggests that Massey’s theorem may be a powerful tool whose uses are not yet fully uncovered.

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References

  1. J. L. Massey, “Shift-register synthesis and BCH decoding”, IEEE Transactions on Information Theory, Vol. 15, pp. 122–127, 1969.

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  3. K. Saints and C. Heegard, “On hyperbolic cascaded Reed-Solomon codes”, Proceedings of the Tenth International Symposium on Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes, San Juan, Puerto Rico, 1993.

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  4. S. Sakata, “Finding a minimal set of linear recurring relations capable of generating a given finite two-dimensional array”, Journal of Symbolic Computation, Vol. 5, pp. 321–337, 1988.

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  6. T. Schaub, A Linear Complexity Approach to Cyclic Codes, Doctor of Technical Sciences Dissertation, ETH Swiss Federal Institute of Technology, Zurich, 1988.

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© 1994 Springer Science+Business Media New York

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Blahut, R.E. (1994). Massey’s Theorem and the Golay Codes. In: Blahut, R.E., Costello, D.J., Maurer, U., Mittelholzer, T. (eds) Communications and Cryptography. The Springer International Series in Engineering and Computer Science, vol 276. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2694-0_5

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  • DOI: https://doi.org/10.1007/978-1-4615-2694-0_5

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6159-6

  • Online ISBN: 978-1-4615-2694-0

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