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Linear \(\ell \)-intersection pairs of codes and their applications

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Abstract

In this paper, a linear \(\ell \)-intersection pair of codes is introduced as a generalization of linear complementary pairs of codes. Two linear codes are said to be a linear \(\ell \)-intersection pair if their intersection has dimension \(\ell \). Characterizations and constructions of such pairs of codes are given in terms of the corresponding generator and parity-check matrices. Linear \(\ell \)-intersection pairs of MDS codes over \({\mathbb {F}}_q\) of length up to \(q+1\) are given for all possible parameters. As an application, linear \(\ell \)-intersection pairs of codes are used to construct entanglement-assisted quantum error correcting codes. This provides a large number of new MDS entanglement-assisted quantum error correcting codes.

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Acknowledgements

The authors would like to thank the anonymous referees for very helpful comments. S. Jitman was supported by the Thailand Research Fund and Silpakorn University under Research Grant RSA6280042.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Victoria, PO Box 1700, STN CSC, Victoria, BC, V8W 2Y2, Canada

    Kenza Guenda & T. Aaron Gulliver

  2. Department of Mathematics, Faculty of Science, Silpakorn University, Nakhon Pathom, 73000, Thailand

    Somphong Jitman & Satanan Thipworawimon

Authors
  1. Kenza Guenda
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  2. T. Aaron Gulliver
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  3. Somphong Jitman
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  4. Satanan Thipworawimon
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Correspondence to Somphong Jitman.

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Communicated by V. D. Tonchev.

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Guenda, K., Gulliver, T.A., Jitman, S. et al. Linear \(\ell \)-intersection pairs of codes and their applications. Des. Codes Cryptogr. 88, 133–152 (2020). https://doi.org/10.1007/s10623-019-00676-z

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  • DOI: https://doi.org/10.1007/s10623-019-00676-z

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