Construction of optimal codes from a class of constacyclic codes
Tóm tắt
In this paper, the structure of
$$(\alpha u+\beta (u-\delta ))$$
-constacyclic codes of length n over the finite commutative non-local ring
$$\frac{{\mathbb {F}}_{p^m}[u]}{\left\langle u^2-\delta u \right\rangle }$$
is provided, where
$$\alpha , \beta $$
and
$$\delta $$
are units of
$${\mathbb {F}}_{p^m}$$
. The structure of dual constacyclic codes is considered and the hull of all such codes is determined. Using that, the Hamming and symbol-pair distances of
$$(\alpha u+\beta (u-\delta ))$$
-constacyclic code over the ring
$$\frac{{\mathbb {F}}_{p^m}[u]}{\left\langle u^2-\delta u \right\rangle }$$
are established for code length
$$p^s$$
. As applications, the MDS and MDS symbol-pair codes among them are completely identified.
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