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Non-Projective Two-Weight Codes.

Sascha Kurz1,2

  • 1Mathematisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany.

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PubMed
Summary
This summary is machine-generated.

The difference between non-zero weights in projective two-weight codes is a field characteristic power. This study extends this finding to non-projective codes and provides binary case enumerations.

Keywords:
linear codestwo-character setstwo-weight codes

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Area of Science:

  • Coding Theory
  • Finite Fields
  • Algebraic Geometry

Background:

  • Projective Fq-linear two-weight codes have known weight difference properties related to field characteristic.
  • Understanding these properties is crucial for error correction and data security applications.

Purpose of the Study:

  • To investigate the weight difference property for non-projective two-weight codes.
  • To extend existing results from projective to non-projective settings.
  • To enumerate feasible parameters for binary non-projective two-weight codes in small dimensions.

Main Methods:

  • Theoretical analysis of linear codes over finite fields.
  • Exploration of code properties under specific conditions.
  • Computational enumeration for small-dimensional binary codes.

Main Results:

  • The property that the difference of non-zero weights is a power of the field characteristic is shown to hold for non-projective two-weight codes under mild additional conditions.
  • Exhaustive enumerations of feasible parameters are provided for small dimensions in the binary case.

Conclusions:

  • The established weight difference property is more general than previously thought.
  • The findings contribute to a deeper understanding of two-weight codes and their parameters.
  • Results pave the way for constructing and analyzing new classes of codes.