Generalized hamming weights of nonlinear codes and the relation to the linear representation

Ilan Reuven, Yair Be'ery

Research output: Contribution to journalArticlepeer-review

Abstract

In this correspondence, we give a new definition of generalized Hamming weights of nonlinear codes and a new interpretation connected with it. These generalized weights are determined by the entropy/length profile of the code. We show that this definition characterizes the performance of nonlinear codes on the wire-tap channel of type II. The new definition is invariant under translates of the code, it satisfies the property of strict monotonicity and the generalized Singleton bound. We check the relations between the generalized weight hierarchies of Z'4 linear codes and their binary image under the Gray map. We also show that the binary image of a Z -linear code is a symmetric, not necessarily rectangular code. Moreover, if this binary image is a linear code then it admits a twisted squaring construction.

Original languageEnglish
Pages (from-to)713-720
Number of pages8
JournalIEEE Transactions on Information Theory
Volume45
Issue number2
DOIs
StatePublished - 1999

Keywords

  • Entropy/length profiles
  • Generalized hamming weights
  • Linear codes over Z4
  • Nonlinear codes
  • Twisted squaring construction

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