On Hamming and b-symbol distance distributions of repeated-root constacyclic codes of length $$4p^s$$ over $${\pmb {\mathbb {F}}}_{p^m}+u {\pmb {\mathbb {F}}}_{p^m}$$

Dinh, Hai Q.; Singh, Abhay Kumar; Thakur, Madhu Kant

doi:10.1007/s12190-020-01456-y

Cited by 2 publications

(2 citation statements)

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“…Dinh et al determined the symbol-triple distances of all the constacyclic codes of length p s over p m in [15]. In [17], Dinh et al determined all the Hamming and b-symbol distances of constacyclic codes of length 4p s over p m + u p m for non-square unit λ and explored all b-symbol MDS codes.…”

Section: Introductionmentioning

confidence: 99%

On symbol-pair distances of repeated-root constacyclic codes of length $$2p^s$$ over $${\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p^m}$$ and MDS symbol-pair codes

Dinh

Singh

Thakur

2021

AAECC

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Let ℜ = p m + u p m with u 2 = 0 , where m, s are positive integers and p is an odd prime. For any invertible element of ℜ , the symbol-pair distances of all -constacyclic codes of length 2p s over ℜ are completely obtained. We identify all symbolpair Maximum Distance Separable (MDS) constacyclic codes of length 2p s over ℜ . As examples, many new symbol-pair codes, as well as symbol-pair MDS codes are constructed. Keywords Repeated-root codes • Symbol-pair MDS codes • Finite chain rings • Constacyclic codes • Symbol-pair distance Mathematics Subject Classification 94B15 • 11T71Authors' names are in alphabetical order. This is a part of Ph.D. work of Mr. M. K. Thakur.

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Section: Introductionmentioning

confidence: 99%

On symbol-pair distances of repeated-root constacyclic codes of length $$2p^s$$ over $${\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p^m}$$ and MDS symbol-pair codes

Dinh

Singh

Thakur

2021

AAECC

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“…In 2020, the Hamming distance of λ-constacyclic codes of length 3p s over R is established in R [15], where λ = α + uβ is not a cube. In 2020, the Hamming distances and b-symbol distances of λ-constacyclic codes of length 4p s over R are determined for p m ≡ 1 (mod 4) and the non-square unit λ [16]. In this paper, we completely symbol-triple distance of λ-constacyclic codes of length 3p s over R, where λ is not a cube in F p m .…”

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On Symbol-Triple Distance of a Class of Constacyclic Codes of Length 3p^s Over F_p^m + uF _p^m

et al. 2023

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Let p = 3 be any prime. In this paper, we completely determine symbol-triple distance of all γ-constacyclic codes of length 3p s over the finite commutative chain ring R = F p m + uF p m , where γ is a unit of R which is not a cube in F p m . We give the necessary and sufficient condition for a symbol-triple γ-constacyclic code to be an MDS symbol-triple code. Using that, we establish all MDS symbol-triple γconstacyclic codes of length 3p s over R. Some examples of the symbol-triple distance of γ-constacyclic codes of length 3p s over R are provided. We also list some new MDS symbol-triple γ-constacyclic codes of length 3p s over R, where γ is not a cube in F p m . INDEX TERMS Constacyclic codes, dual codes, chain rings, MDS symbol-triple codes, symbol-triple codes.

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On Hamming and b-symbol distance distributions of repeated-root constacyclic codes of length $$4p^s$$ over $${\pmb {\mathbb {F}}}_{p^m}+u {\pmb {\mathbb {F}}}_{p^m}$$

Cited by 2 publications

References 26 publications

On symbol-pair distances of repeated-root constacyclic codes of length $$2p^s$$ over $${\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p^m}$$ and MDS symbol-pair codes

On symbol-pair distances of repeated-root constacyclic codes of length $$2p^s$$ over $${\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p^m}$$ and MDS symbol-pair codes

On Symbol-Triple Distance of a Class of Constacyclic Codes of Length 3p^s Over F_p^m + uF _p^m

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On Hamming and b-symbol distance distributions of repeated-root constacyclic codes of length $$4p^s$$ over $${\pmb {\mathbb {F}}}_{p^m}+u {\pmb {\mathbb {F}}}_{p^m}$$

Cited by 2 publications

References 26 publications

On symbol-pair distances of repeated-root constacyclic codes of length $$2p^s$$ over $${\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p^m}$$ and MDS symbol-pair codes

On symbol-pair distances of repeated-root constacyclic codes of length $$2p^s$$ over $${\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p^m}$$ and MDS symbol-pair codes

On Symbol-Triple Distance of a Class of Constacyclic Codes of Length 3ps Over F pm + uF pm

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On Symbol-Triple Distance of a Class of Constacyclic Codes of Length 3p^s Over F_p^m + uF _p^m