Additive and linear conjucyclic codes over \(\mathbb{F}_4\)
In this paper, the authors are interested in linear and additive conjucyclic codes over the finite field \(\mathbb{F}_4\). There is produced a special kind of duality for which the orthogonal (with respect to that duality) of conjucyclic codes is conjucyclic. Moreover, there is shown that this is not the case for other standard dualities. The authors prove that additive conjucyclic codes are the only non-trivial conjucyclic codes over \(\mathbb{F}_4\) and they classify these codes by linear algebraic approach. Finally, there is shown that additive conjucyclic codes of length \(n\) over \(\mathbb{F}_4\) are isomorphic to binary cyclic codes of length \(2n\).
scientific article; zbMATH DE number 7461984