Constructions of Formally Self-Dual Codes over Z4 and Their Weight Enumerators

Jinjoo Yoo, Yoonjin Lee, Boreum Kim

Research output: Contribution to journalArticlepeer-review

Abstract

We present three explicit methods for construction of formally self-dual codes over Z4. We characterize relations between Lee weight enumerators of formally self-dual codes of length n+Z4 and those of length n+2; the first two construction methods are based on these relations. The last construction produces free formally self-dual codes over Z4. Using these three constructions, we can find free formally self-dual codes over Z4, as well as non-free formally self-dual codes over Z4 of all even lengths. We find free or non-free formally self-dual codes over Z4 of lengths up to ten using our constructions. In fact, we obtain 46 inequivalent formally self-dual codes whose minimum Lee weights are larger than self-dual codes of the same length. Furthermore, we find 19 non-linear extremal binary formally self-dual codes of lengths 12, 16, and 20, up to equivalence, from formally self-dual codes over Z4 by using the Gray map.

Original languageEnglish
Article number8063420
Pages (from-to)7667-7675
Number of pages9
JournalIEEE Transactions on Information Theory
Volume63
Issue number12
DOIs
StatePublished - Dec 2017

Keywords

  • Formally self-dual code
  • Gray map
  • Lee weight enumerator
  • code over Z
  • non-linear extremal binary formally self-dual code

Fingerprint

Dive into the research topics of 'Constructions of Formally Self-Dual Codes over Z4 and Their Weight Enumerators'. Together they form a unique fingerprint.

Cite this