QUANTUM CODES WITH IMPROVED MINIMUM DISTANCE - Kolotoglu, Emre; Sari, Mustafa (KOREAN MATHEMATICAL SOC, 2019)
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].
Keywords: quantum codes; cyclic codes; constacyclic codes; cyclotomic cosets; MDS CODES; CONSTRUCTION; Mathematics