Self-orthogonal codes over Z4 arising from the chain ring Z4[u]/〈u2+1〉

Boran Kim, Nayoung Han, Yoonjin Lee

Research output: Contribution to journalArticlepeer-review


We find a building-up type construction method for self-orthogonal codes over Z4 arising from the chain ring Z4[u]/〈u2+1〉. Our construction produces self-orthogonal codes over Z4 with increased lengths and free ranks from given self-orthogonal codes over Z4 with smaller lengths and free ranks; in the most of the cases their minimum weights are also increased. Furthermore, any self-orthogonal code over Z4 with generator matrix subject to certain conditions can be obtained from our construction. Employing our construction method, we obtain at least 125 new self-orthogonal codes over Z4 up to equivalence; among them, there are 35 self-orthogonal codes which are distance-optimal. Furthermore, we have eight self-orthogonal codes, which are distance-optimal among all linear codes over Z4 with the same type. As a method, we use additive codes over the finite ring Z4[u]/〈u2+1〉 with generator matrices G satisfying GGT=O, and we use a new Gray map from Z4[u]/〈u2+1〉 to Z43 as well.

Original languageEnglish
Article number101972
JournalFinite Fields and their Applications
StatePublished - Feb 2022


  • Additive code
  • Chain ring
  • Gray map
  • Optimal code
  • Self-orthogonal code


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