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Optimal strongly conflict-avoiding codes of even length and weight three

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Abstract

Strongly conflict-avoiding codes (SCACs) are employed in a slot-asynchronous multiple-access collision channel without feedback to guarantee that each active user can send at least one packet successfully in the worst case within a fixed period of time. By the assumption that all users are assigned distinct codewords, the number of codewords in an SCAC is equal to the number of potential users that can be supported. SCACs have different combinatorial structure compared with conflict-avoiding codes (CACs) due to additional collisions incurred by partially overlapped transmissions. In this paper, we establish upper bounds on the size of SCACs of even length and weight three. Furthermore, it is shown that some optimal CACs can be used to construct optimal SCACs of weight three.

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Acknowledgments

The authors would like to express their gratitude to the referees for their helpful comments in improving the presentation of this paper. This work was supported by the Hong Kong RGC Earmaked Grant CUHK414012, the National Natural Science Foundation of China (No. 61301107 and 61174060), the Shenzhen Knowledge Innovation Program JCYJ20130401-172046453 and the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20133219120010).

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Authors and Affiliations

  1. School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing, China

    Yijin Zhang

  2. Department of Mathematics, National Taiwan Normal University, Taipei, 116, Taiwan

    Yuan-Hsun Lo

  3. Department of Information Engineering, The Chinese University of Hong Kong, Shatin, New Town, Hong Kong

    Wing Shing Wong

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  1. Yijin Zhang
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  2. Yuan-Hsun Lo
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  3. Wing Shing Wong
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Correspondence to Yuan-Hsun Lo.

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Communicated by C. J. Colbourn.

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Zhang, Y., Lo, YH. & Wong, W.S. Optimal strongly conflict-avoiding codes of even length and weight three. Des. Codes Cryptogr. 79, 367–382 (2016). https://doi.org/10.1007/s10623-015-0057-7

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  • DOI: https://doi.org/10.1007/s10623-015-0057-7

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