QUANTUM CODES WITH IMPROVED MINIMUM DISTANCE


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Kolotoğlu E. , Sarı M.

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, vol.56, pp.609-619, 2019 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 56
  • Publication Date: 2019
  • Doi Number: 10.4134/bkms.b180295
  • Title of Journal : BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
  • Page Numbers: pp.609-619

Abstract

The methods for constructing quantum codes is not always sufficient by itself. Also, the constructed quantum codes as in the classical coding theory have to enjoy a quality of its parameters that play a very important role in recovering data efficiently. In a very recent study quantum construction and examples of quantum codes over a finite field of order q are presented by La Garcia in [14]. Being inspired by La Garcia's the paper, here we extend the results over a finite field with q(2) elements by studying necessary and sufficient conditions for constructions quantum codes over this field. We determine a criteria for the existence of q(2)-cyclotomic cosets containing at least three elements and present a construction method for quantum maximum-distance separable (MDS) codes. Moreover, we derive a way to construct quantum codes and show that this construction method leads to quantum codes with better parameters than the ones in [14].