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Local duality theorem for q-ary 1-perfect codes

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Abstract

In this paper, we derive the relationship between local weight enumerator of q-ary 1-perfect code in a face and that in the orthogonal face. As an application of our result, we compute the local weight enumerators of a shortened, doubly-shortened, and triply-shortened q-ary 1-perfect code.

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Authors and Affiliations

  1. Department of Mathematics, POSTECH, Pohang, 790-784, S. Korea

    Soohak Choi & Hyun Kwang Kim

  2. The Institute of Mathematical Sciences, Ewha Womans University, 11-1, Daehyun-Dong, Seodaemun-Gu, Seoul, 120-750, S. Korea

    Jong Yoon Hyun

Authors
  1. Soohak Choi
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  2. Jong Yoon Hyun
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  3. Hyun Kwang Kim
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Corresponding author

Correspondence to Jong Yoon Hyun.

Additional information

Communicated by V. A. Zinoviev.

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Choi, S., Hyun, J.Y. & Kim, H.K. Local duality theorem for q-ary 1-perfect codes. Des. Codes Cryptogr. 70, 305–311 (2014). https://doi.org/10.1007/s10623-012-9683-5

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  • DOI: https://doi.org/10.1007/s10623-012-9683-5

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