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On Generalized Hamming Weights and the Covering Radius of Linear Codes

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Book cover Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4851))

Abstract

We prove an upper bound on the covering radius of linear codes over \({\mathbb{F}_q}\)in terms of their generalized Hamming weights. We show that this bound is strengthened if we know that the codes satisfy the chain condition or a partial chain condition. We show that this bound improves all prior bounds. Necessary conditions for equality are also presented.

Several applications of our bound are presented. We give tables of improved bounds on the covering radius of many cyclic codes using their generalized Hamming weights. We show that most cyclic codes of length ≤ 39 satisfy the chain condition or partial chain condition up to level 5. We use these results to derive tighter bounds on the covering radius of cyclic codes.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Puerto Rico (UPR), Rio Piedras Campus, P.O. Box: 23355, San Juan, PR 00931 - 3355,  

    H. Janwa

  2. Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, 208016, India

    A. K. Lal

Authors
  1. H. Janwa
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  2. A. K. Lal
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Serdar Boztaş Hsiao-Feng (Francis) Lu

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© 2007 Springer-Verlag Berlin Heidelberg

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Janwa, H., Lal, A.K. (2007). On Generalized Hamming Weights and the Covering Radius of Linear Codes. In: Boztaş, S., Lu, HF.(. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2007. Lecture Notes in Computer Science, vol 4851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77224-8_40

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  • DOI: https://doi.org/10.1007/978-3-540-77224-8_40

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77223-1

  • Online ISBN: 978-3-540-77224-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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