Abstract
Polycyclic codes are ideals in quotients of polynomial rings by a principal ideal. Special cases are cyclic and constacyclic codes.A MacWilliams relation between such a code and its annihilator ideal is derived. An infinite family of binary self-dual codes that are also formally self-dualin the classical sense is exhibited.We show that right polycyclic codes are left polycyclic codes with different(explicit) associate vectors and characterize the casewhen a code is both left and right polycyclic for the same associate polynomial. A similar study is led for sequential codes.
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