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On the duality and the direction of polycyclic codes. (English) Zbl 1353.94085

Summary: 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-dual in the classical sense is exhibited. We show that right polycyclic codes are left polycyclic codes with different (explicit) associate vectors and characterize the case when a code is both left and right polycyclic for the same associate polynomial. A similar study is led for sequential codes.

MSC:

94B15 Cyclic codes
94B05 Linear codes (general theory)
94B65 Bounds on codes
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References:

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