Cyclotomic trace codes

Authors

Dean Crnkovic, University of Rijeka
Andrea Svob, University of Rijeka
Vladimir Tonchev, Michigan Technological UniversityFollow

Document Type

Article

Publication Date

8-13-2019

Department

Department of Mathematical Sciences

Abstract

A generalization of Ding’s construction is proposed that employs as a defining set the collection of the sth powers (s ≥ 2) of all nonzero elements in GF(p^m), where p ≥ 2 is prime. Some of the resulting codes are optimal or near-optimal and include projective codes over GF(4) that give rise to optimal or near optimal quantum codes. In addition, the codes yield interesting combinatorial structures, such as strongly regular graphs and block designs.

Publisher's Statement

©2019 by the authors. Article deposited here in compliance with publisher policies. Publisher's version of record: https://doi.org/10.3390/a12080168

Publication Title

algorithms

Recommended Citation

Crnkovic, D., Svob, A., & Tonchev, V. (2019). Cyclotomic trace codes. algorithms, 12(8). http://doi.org/10.3390/a12080168
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/483

Version

Publisher's PDF