Hamming distance of repeated-root constacyclic codes of length $$2p^s$$ over $${\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p^m}$$

MDS Constacyclic Codes and MDS Symbol-Pair Constacyclic Codes

“…On the other hand, the Hamming distance of all cyclic codes of length 2p s over F p m was provided in [50]. After that, [26] computed the Hamming distances of all λ-constacyclic codes of length 2p s over F p m + uF p m , and identify all the MDS codes among them. The authors of [26] also gave some new codes which have better parameters than existing ones.…”

“…After that, [26] computed the Hamming distances of all λ-constacyclic codes of length 2p s over F p m + uF p m , and identify all the MDS codes among them. The authors of [26] also gave some new codes which have better parameters than existing ones. However, in the papers [26], [28], [39], they had some errors on codes of Type 3.…”

“…The authors of [26] also gave some new codes which have better parameters than existing ones. However, in the papers [26], [28], [39], they had some errors on codes of Type 3. For more details, [39,Theorem 12] and [28,Theorem 7] had an error on the generator of Type 3 codes, as the exponent i of (x − λ 0 ) i F should be T .…”

“…We also see that [27,Theorem 8] had also some errors. In addition, in [26], the authors studied Hamming distance of repeatedroot constacyclic codes of length 2p s over R but the result on Hamming distance of Type 3 codes is not correct.…”

Symbol-Pair Distance of Repeated-Root Constacyclic Codes of Prime Power Lengths over \({{\mathbb{F}_{p^m}[u]}/{\langle u^3\rangle}}\)

“…When a = 2, there is significant literature on constacyclic codes over rings F p m [u]/ u 2 = F p m + uF p m for various prime p and positive integers m (see, e.g., [15][16][17][18][19][20][21][22][23].). In particular, the structure of and symbol-pair distance distibution of all constacyclic codes of length p s over F p m + uF p m were completely determined in [7,8,17].…”