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Open AccessArticle

Cyclotomic Trace Codes

1
Department of Mathematics, University of Rijeka, Radmile Matejčić 2, 51000 Rijeka, Croatia
2
Department of Mathematical Sciences, Michigan Technological University, Houghton, MI 49931, USA
*
Author to whom correspondence should be addressed.
Algorithms 2019, 12(8), 168; https://doi.org/10.3390/a12080168
Received: 20 June 2019 / Revised: 3 August 2019 / Accepted: 10 August 2019 / Published: 13 August 2019
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PDF [249 KB, uploaded 13 August 2019]

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 G F ( p m ) , where p 2 is prime. Some of the resulting codes are optimal or near-optimal and include projective codes over G F ( 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. View Full-Text
Keywords: linear code; two-weight code; strongly regular graph; block design linear code; two-weight code; strongly regular graph; block design
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Crnković, D.; Švob, A.; Tonchev, V.D. Cyclotomic Trace Codes. Algorithms 2019, 12, 168.

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