Maximum distance separable repeated-root constacyclic codes over $$\mathbb {F}_{2^m}+u\mathbb {F}_{2^m}$$ with respect to the Lee distance
Springer Science and Business Media LLC - Trang 1-15 - 2022
Tóm tắt
Maximum distance separable (MDS) codes have the highest possible error-correcting capability among codes with the same length and size. Let
$$\gamma $$
be nonzero in
$$\mathbb {F}_{2^m}.$$
We consider all cyclic and
$$(1+u\gamma )$$
-constacyclic codes of length
$$2^s$$
over
$$\mathbb {F}_{2^m}+u\mathbb {F}_{2^m}$$
with their Lee distance and investigate all the cases whether the corresponding Gray images are MDS by giving an analogue of the Singleton bound for codes over
$$\mathbb {F}_{2^m}+u\mathbb {F}_{2^m}$$
with the Lee distance through Gray map.
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