A Criterion for Designs in {\tf="P101461" Z}_4-codes on the Symmetrized Weight Enumerator

  • Authors:

  • Kenichiro Tanabe

  • Affiliations:

  • Institute of Mathematics, University of Tsukuba, 1-1-1 Ten-nou-dai, Tsukuba City, 305–8571, Japan tanabe@math.tsukuba.ac.jp

  • Venue:
  • Designs, Codes and Cryptography
  • Year:
  • 2003

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Abstract

The Assmus–Mattson theorem is known as a method to find designs in linear codes over a finite field. It is an interesting problem to find an analog of the theorem for Z4-codes. In a previous paper, the author gave a candidate of the theorem. The purpose of this paper is to give an improvement of the theorem. It is known that the lifted Golay code over Z4 contains 5-designs on Lee compositions. The improved method can find some of those without computational difficulty and without the help of a computer.