Advertisement
Published in:
01-12-2020 | Original Research
On Hamming and b-symbol distance distributions of repeated-root constacyclic codes of length \(4p^s\) over \({\pmb {\mathbb {F}}}_{p^m}+u {\pmb {\mathbb {F}}}_{p^m}\)
Published in: Journal of Applied Mathematics and Computing | Issue 1-2/2021
Log inActivate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
Abstract
Let p be a prime such that \(p^m \equiv 1\pmod {4}\), and \(\mathcal{R}=\mathbb F_{p^m}+u\mathbb F_{p^m}\). For any non-square unit \(\lambda \) of \(\mathcal{R}\), the Hamming and b-symbol distances of all \(\lambda \)-constacyclic codes of length \(4p^s\) over \(\mathcal{R}\) are completely determined. As examples, several good codes with new parameters are constructed. We also identified all Maximum Distance Separable constacyclic codes of length \(4p^s\) over \(\mathcal{R}\) with respect to the Hamming distance as well as the b-symbol distance. Also, we got some non-trivial MDS b-symbol Type 3, \(\gamma \)-constacyclic codes of length \(4p^s\) codes over \(\mathcal{R}\) with respect to b-symbol distance for \(b=4\).