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AIMS Mathematics

2016, Volume 1, Issue 2: 96-101. doi: 10.3934/Math.2016.2.96
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Research article

On deep holes of generalized Reed-Solomon codes

  • Mathematical College, Sichuan University, Chengdu 610064, P.R. China
  • Received: 16 May 2016 Accepted: 20 June 2016 Published: 28 June 2016

  • Determining deep holes is an important topic in decoding Reed-Solomon codes. In a previous paper [8], we showed that the received word u is a deep hole of the standard Reed-Solomon codes [q-1, k]q if its Lagrange interpolation polynomial is the sum of monomial of degree q-2 and a polynomial of degree at most k-1. In this paper, we extend this result by giving a new class of deep holes of the generalized Reed-Solomon codes.

    Citation: Shaofang Hong, Rongjun Wu. On deep holes of generalized Reed-Solomon codes[J]. AIMS Mathematics, 2016, 1(2): 96-101. doi: 10.3934/Math.2016.2.96

    Related Papers:

  • Determining deep holes is an important topic in decoding Reed-Solomon codes. In a previous paper [8], we showed that the received word u is a deep hole of the standard Reed-Solomon codes [q-1, k]q if its Lagrange interpolation polynomial is the sum of monomial of degree q-2 and a polynomial of degree at most k-1. In this paper, we extend this result by giving a new class of deep holes of the generalized Reed-Solomon codes.


    加载中
    [1] Q. Cheng and E. Murray, On deciding deep holes of Reed-Solomon codes Proceedings of TAMC 2007, LNCS 4484, Springer, Berlin, 296-305.
    [2] V. Guruswami and M. Sudan, Improved decoding of Reed-Solomon and algebraic-geometry codes IEEE Trans. Inform. Theory, (1999), 1757-1767.
    [3] V. Guruswami and A. Vardy, Maximum-likelihood decoding of Reed-Solomon codes is NP-hard IEEE Trans. Inform. Theory, (2005), 2249-2256.
    [4] J. Li and D. Wan, On the subset sum problem over finite fields Finite Fields Appls., (2008), 911-929.
    [5] Y. Li and D. Wan, On error distance of Reed-Solomon codes Science in China Series A: Mathematics, {\bf 51} (2008), 1982-1988.
    [6] M. Sudan, Decoding of Reed-Solomon codes beyond the error-correction bound J. Complexity, (1997), 180-193.
    [7] R. Wu, On deep holes of Reed-Solomon codes and nonlinearity of rotation symmetric Boolean functions PhD. Thesis, Sichuan University, April, 2012.
    [8] R. Wu and S. Hong, On deep holes of standard Reed-Solomon codes Sci. Math. China, (2012), 2447-2455.
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  • © 2016 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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