English

An infinite class of quantum codes derived from duadic constacyclic codes

Information Theory 2024-05-28 v2 math.IT

Abstract

We present a family of quantum stabilizer codes using the structure of duadic constacyclic codes over F4\mathbb{F}_4. Within this family, quantum codes can possess varying dimensions, and their minimum distances are lower bounded by a square root bound. For each fixed dimension, this allows us to construct an infinite sequence of binary quantum codes with a growing minimum distance. Additionally, we prove that this family of quantum codes includes an infinite subclass of degenerate codes. We also introduce a technique for extending splittings of duadic constacyclic codes, providing new insights into the minimum distance and minimum odd-like weight of specific duadic constacyclic codes. Finally, we provide numerical examples of some quantum codes with short lengths within this family.

Keywords

Cite

@article{arxiv.2312.06504,
  title  = {An infinite class of quantum codes derived from duadic constacyclic codes},
  author = {Reza Dastbasteh and Josu Etxezarreta Martinez and Andrew Nemec and Antonio deMarti iOlius and Pedro Crespo Bofill},
  journal= {arXiv preprint arXiv:2312.06504},
  year   = {2024}
}

Comments

31 pages, 2 tables

R2 v1 2026-06-28T13:47:18.111Z