Algebraic Structures of Constacyclic Codes Over Finite Chain Rings and Power Series Rings
- 3 Downloads
Let R be a chain ring with the maximal ideal \(\langle \gamma \rangle\). In this paper, we shall study \((r_1+r_2\gamma )\)-constacyclic codes of arbitrary length over R, where \(r_1, r_2\) are units in R. We shall obtain the generators of these codes and their duals. Moreover, a minimal spanning set (and so a generator matrix) for a constacyclic code is obtained. We shall determine the minimum Hamming distance of a constacyclic code over the chain ring R. At last, we shall study some constacyclic codes over formal power series rings. The minimal spanning set for these codes are also established.
KeywordsLinear code Constacyclic code Finite chain ring Formal power series ring Minimum Hamming distance
Mathematics Subject Classification94B05 94A55 94B15 58F15 58F17
- Matsumura Commutative (1990) Ring theory. Cambridge University Press, CambridgeGoogle Scholar
- Prange E (1957) Cyclic error-correcting codes in two symbols. Technical report TN-57-103. Air Force Cambridge Research Center, CambridgeGoogle Scholar
- Roman S (1974) Coding and information theory. Marcel Dekker, New YorkGoogle Scholar