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New Upper Bounds on the Size of Binary Codes

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Abstract

Any subset C of the group \({\mathbb {Z}}_2^n\) is called a binary code of length n and its elements are called codewords. Let A(n, d) be the maximum size of a binary code of length n in which the Hamming distance of any two codewords is at least d. In this paper, using the Delsarte–Hoffman bound and some tools from algebraic graph theory, we provide new upper bounds on A(n, d).

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References

  • Ahmadi B (2013) Maximum intersecting families of permutations. University of Regina, Ph.D. thesis

  • Ahmadi B, Meagher K (2014) A new proof for the Erdős-Ko-Rado Theorem for the alternating group. Discret Math 324:28–40

    Article  MATH  Google Scholar 

  • Ahmadi B, Meagher K (2015) The Erdős-Ko-Rado property for some permutation groups. Aust J Comb 61(1):23–41

    MATH  Google Scholar 

  • Biggs N (1993) Algebraic graph theory. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Diaconis P, Shahshahani M (1981) Generating a random permutation with random transpositions. Probab Theory Relat Fields 57(2):159–179

    MathSciNet  MATH  Google Scholar 

  • El Rouayheb SY, Georghiades CN, Soljanin E, Sprintson A (2007) Bounds on codes based on graph theory. In: Information Theory, 2007. ISIT 2007. IEEE International Symposium on, p 1876–1879. IEEE, 2007

  • Fulton W, Harris J (2013) Representation theory: a first course, vol 129. Springer Science & Business Media, New York

    MATH  Google Scholar 

  • Godsil C, Meagher K (2016) An algebraic proof of the Erdős-Ko-Rado theorem for intersecting families of perfect matchings. Ars Mathematica Contemporanea 12(2):205–217

    Article  MATH  Google Scholar 

  • MacWilliams FJ, Sloane NJA (1977) The theory of error-correcting codes. Elsevier, Amsterdam

    MATH  Google Scholar 

  • Meagher K, Spiga P (2011) An Erdős-Ko-Rado theorem for the derangement graph of PGL(2, q) acting on the projective line. J Comb Theory Ser A 118(2):532–544

    Article  MATH  Google Scholar 

  • Meagher K, Spiga P, Tiep PH (2016) An An Erdős-Ko-Rado theorem for finite 2-transitive groups. Eur J Comb 55:100–118

    Article  MATH  Google Scholar 

  • Newman MW (2004) Independent sets and Eigenspaces. University of Waterloo, Ph.D. thesis

  • Sloane NJA (1989) Unsolved problems in graph theory arising from the study of codes. Graph Theory Notes NY 18:11–20

    Google Scholar 

  • Trevisan L (2016) Spectral methods and expanders. University Lecture, U.C. Berkeley

Download references

Acknowledgements

The first author would like to thank the financial support provided by the Iranian National Elites’ Foundation.

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Authors and Affiliations

  1. Department of Mathematics, Shiraz University, Shiraz, 71457-44776, Iran

    Bahman Ahmadi & Fatemeh Alinaghipour

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  1. Bahman Ahmadi
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  2. Fatemeh Alinaghipour
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Correspondence to Fatemeh Alinaghipour.

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Ahmadi, B., Alinaghipour, F. New Upper Bounds on the Size of Binary Codes. Iran J Sci Technol Trans Sci 43, 923–928 (2019). https://doi.org/10.1007/s40995-017-0468-6

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  • DOI: https://doi.org/10.1007/s40995-017-0468-6

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