A note on nonlinear Xing codes

Yaron Shany*, Yair Be'ery

*Corresponding author for this work

Research output: Contribution to journalLetterpeer-review

Abstract

Nonlinear Xing codes are considered. It is shown that Xing codes of length p - 1 (where p is a prime) are subcodes of cosets of Reed-Solomon codes whose minimum distance equals Xing's lower bound on the minimum distance. This provides a straightforward proof for the lower bound on the minimum distance of the codes. The alphabet size of Xing codes is restricted not to be larger than the characteristic of the relevant finite field Fr. It is shown that codes with the same length and the same lower bounds on the size and minimum distance as Xing codes exist for any alphabet size not exceeding the size r of the relevant finite field, thus extending Xing's results.

Original languageEnglish
Pages (from-to)699-700
Number of pages2
JournalIEEE Transactions on Information Theory
Volume50
Issue number4
DOIs
StatePublished - Apr 2004

Keywords

  • Reed-Solomon codes
  • Xing codes

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