On quantum codes via cyclic codes of arbitrary length over š¯”½4 + uš¯”½4
Amit Sharma, Ramakrishna Bandi, Maheshanand Bhaintwal Ā· Discrete Mathematics Algorithms and Applications Ā· 2018
In this paper, we study cyclic codes over [Formula: see text]. A necessary and sufficient condition for a cyclic code over [Formula: see text] to contain its dual is determined. The odd and even length cases are discussed separately to obtain above condition. It is shown that Gray image of a cyclic code over [Formula: see text] containing its dual is a linear code over [Formula: see text] which also contains its dual. We have then obtained the parameters of corresponding CSS-quantum codes over [Formula: see text]. By augmentation, we construct codes with dual-containing property from codes of smaller size containing their duals. Through this construction, we have obtained some optimal quantum codes over [Formula: see text]. Some examples have been given to illustrate the results.