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On Minimal and Quasi-minimal Linear Codes

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Cryptography and Coding (IMACC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 8308))

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Abstract

Minimal linear codes are linear codes such that the support of every codeword does not contain the support of another linearly independent codeword. Such codes have applications in cryptography, e.g. to secret sharing. We here study minimal codes, give new bounds and properties and exhibit families of minimal linear codes. We also introduce and study the notion of quasi-minimal linear codes, which is a relaxation of the notion of minimal linear codes, where two non-zero codewords have the same support if and only if they are linearly dependent.

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Author information

Authors and Affiliations

  1. CNRS LTCI, Télécom ParisTech, France

    Gérard D. Cohen & Alain Patey

  2. Department of Mathematics, LAGA (Laboratoire Analyse, Géometrie et Applications), UMR 7539, CNRS, University of Paris VIII, Sorbonne Paris Cité, France

    Sihem Mesnager

  3. Morpho, France

    Alain Patey

  4. Identity and Security Alliance (The Morpho and Télécom ParisTech Research Center), France

    Gérard D. Cohen & Alain Patey

Authors
  1. Gérard D. Cohen
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  2. Sihem Mesnager
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  3. Alain Patey
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Editor information

Editors and Affiliations

  1. Dept. of Computer Science, University of Bristol, Woodland Road, BS8 1UB, Bristol, UK

    Martijn Stam

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Cohen, G.D., Mesnager, S., Patey, A. (2013). On Minimal and Quasi-minimal Linear Codes. In: Stam, M. (eds) Cryptography and Coding. IMACC 2013. Lecture Notes in Computer Science, vol 8308. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45239-0_6

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  • DOI: https://doi.org/10.1007/978-3-642-45239-0_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-45238-3

  • Online ISBN: 978-3-642-45239-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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