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Cyclotomic trace codes

Algorithms, ISSN: 1999-4893, Vol: 12, Issue: 8
2019
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Algorithms, Vol. 12, Pages 168: Cyclotomic Trace Codes

Algorithms, Vol. 12, Pages 168: Cyclotomic Trace Codes Algorithms doi: 10.3390/a12080168 Authors: Dean Crnković Andrea Švob Vladimir D. Tonchev A generalization of Ding’s construction is

Article Description

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), 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.

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