Results 1 to 10 of about 1,045 (128)
Asymmetric Entanglement-Assisted Quantum MDS Codes Constructed from Constacyclic Codes. [PDF]
Entropy (Basel), 2023 Due to the asymmetry of quantum errors, phase-shift errors are more likely to occur than qubit-flip errors. Consequently, there is a need to develop asymmetric quantum error-correcting (QEC) codes that can safeguard quantum information transmitted ...
Chen J +7 more
europepmc +2 more sources
MDS Constacyclic Codes and MDS Symbol-Pair Constacyclic Codes [PDF]
IEEE Access, 2021 Symbol-pair codes are used to protect against symbol-pair errors in high density data storage systems. One of the most important tasks in symbol-pair coding theory is to design MDS codes.
Hai Q. Dinh +3 more
doaj +2 more sources
Skew Constacyclic Codes over a Non-Chain Ring. [PDF]
Entropy (Basel), 2023 In this paper, we investigate the algebraic structure of the non-local ring Rq=Fq[v]/⟨v2+1⟩ and identify the automorphisms of this ring to study the algebraic structure of the skew constacyclic codes and their duals over this ring. Furthermore, we give a
Köroğlu ME, Sarı M.
europepmc +2 more sources
Quantum Codes from Galois Hulls of Constacyclic Codes over a Finite Non-Chain Ring. [PDF]
Entropy (Basel)We study the algebraic structures of constacyclic codes over a new finite non-chain ring R and their l-Galois dual codes based on a new Gray map ϕ and determine the dimensions of the l-Galois hull of constacyclic codes over R.
Zhang E, Kong B, Zheng X.
europepmc +2 more sources
Quantum Codes Obtained from Skew ϱ‐λ‐Constacyclic Codes over Rk
Quantum Engineering, Volume 2023, Issue 1, 2023., 2023 Let Rk=Fqu1,u2,⋯,uk/
Bo Kong +4 more
wiley +1 more source
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 Over finite local Frobenius non-chain rings of length 5 and nilpotency index 4 and when the length of the code is relatively prime to the characteristic of the residue field of the ring, the structure of the dual of γ-constacyclic codes is established ...
Castillo-Guillén C. A. +1 more
doaj +1 more source
Characterizations and Properties of Monic Principal Skew Codes over Rings
Security and Communication Networks, Volume 2022, Issue 1, 2022., 2022 Let A be a ring with identity, σ a ring endomorphism of A that maps the identity to itself, δ a σ‐derivation of A, and consider the skew‐polynomial ring A[X; σ, δ]. When A is a finite field, a Galois ring, or a general ring, some fairly recent literature used A[X; σ, δ] to construct new interesting codes (e.g., skew‐cyclic and skew‐constacyclic codes ...
Mhammed Boulagouaz +2 more
wiley +1 more source
Matrix‐Product Codes over Commutative Rings and Constructions Arising from (σ, δ)‐Codes
Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 A well‐known lower bound (over finite fields and some special finite commutative rings) on the Hamming distance of a matrix‐product code (MPC) is shown to remain valid over any commutative ring R. A sufficient condition is given, as well, for such a bound to be sharp. It is also shown that an MPC is free when its input codes are all free, in which case
Mhammed Boulagouaz +2 more
wiley +1 more source
Lower Bound on the Minimum Distance of Single-Generator Quasi-Twisted Codes
Mathematics, 2023 We recall a classic lower bound on the minimum Hamming distance of constacyclic codes over finite fields, analogous to the well-known BCH bound for cyclic codes.
Adel Alahmadi +2 more
doaj +1 more source
Repeated-Root Constacyclic Codes Over the Chain Ring Fpm[u]/⟨u3⟩
IEEE Access, 2020 Let Z = Fpm[u]/(u3) be the finite commutative chain ring, where p is a prime, m is a positive integer and Fpm is the finite field with pm elements. In this paper, we determine all repeated-root constacyclic codes of arbitrary lengths over Z and their ...
Tania Sidana, Anuradha Sharma
doaj +1 more source