Complementary dual skew polycyclic codes and their applications to EAQECCs

For integers e >= 2, m >= 1 and a prime p, consider the ring A(e) = F-q + uF(q) + center dot center dot center dot + u(e-1)F(q), u(e) = u where q = p(m) and e satisfies q equivalent to 1 (mod e- 1). This work investigates skew polycyclic codes over A(e). Using the idempotent decomposition technique, we present the generator polynomial and generator matrix of skew polycyclic codes over A(e). Then we determine the necessary and sufficient conditions for these codes to be self-dual and derive some conditions under which skew polycyclic codes satisfy the complementary duality property. Further, we define a Gray map and investigate the Gray image of an LCD (or self-dual) code over A(e). Besides, we also present a construction of LCD codes from self-dual codes (see Theorem 13). Finally, several examples of entanglement-assisted quantum error-correcting codes obtained from LCD codes are provided.