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Binary cyclic codes with two primitive nonzeros

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Abstract

In this paper, we make some progress towards a well-known conjecture on the minimum weights of binary cyclic codes with two primitive nonzeros. We also determine the Walsh spectrum of Tr(x d) over \(\mathbb{F}_{2^m }\) in the case where m = 2t, d = 3+2t+1 and gcd(d, 2m − 1) = 1.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, China

    Tao Feng

  2. Department of Mathematical Sciences, National University of Singapore, Kent Ridge, 119260, Singapore

    KaHin Leung

  3. Department of Mathematical Sciences, University of Delaware, Newark, DE, 19716, USA

    Qing Xiang

Authors
  1. Tao Feng
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  2. KaHin Leung
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  3. Qing Xiang
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Correspondence to Qing Xiang.

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Feng, T., Leung, K. & Xiang, Q. Binary cyclic codes with two primitive nonzeros. Sci. China Math. 56, 1403–1412 (2013). https://doi.org/10.1007/s11425-013-4668-z

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  • DOI: https://doi.org/10.1007/s11425-013-4668-z

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