An infinite class of quantum codes derived from duadic constacyclic codes
Abstract
We present a family of quantum stabilizer codes using the structure of duadic constacyclic codes over . 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.
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