Results 1 to 10 of about 4,270,277 (317)
New Construction of Maximum Distance Separable (MDS) Self-Dual Codes over Finite Fields [PDF]
Entropy, 2019 Maximum distance separable (MDS) self-dual codes have useful properties due to their optimality with respect to the Singleton bound and its self-duality.
Aixian Zhang, Zhe Ji
doaj +2 more sources
On Quasi-Cyclic Codes of Index 3 [PDF]
EntropyQuasi-cyclic codes of index 3 over finite fields are studied. We give a classification of such codes. Their duals with respect to the Euclidean and Hermitian inner products are investigated.
Kanat Abdukhalikov, Rasha M. Shat
doaj +2 more sources
Symplectic QSD, LCD, and ACD Codes over a Non-Commutative Non-Unitary Ring of Order Nine [PDF]
EntropyWe introduce quasi self-dual (QSD), linear complementary dual (LCD), and additive complementary dual (ACD) codes for the symplectic inner product over a non-commutative non-unitary ring of order 9. We establish connections with symplectic–self-orthogonal
Sarra Manseri +3 more
doaj +2 more sources
New extremal singly even self-dual codes of lengths $64$ and $66$ [PDF]
Journal of Algebra Combinatorics Discrete Structures and Applications, 2017 For lengths $64$ and $66$, we construct extremal singly even self-dual codes with weight enumerators for which no extremal singly even self-dual codes were previously known to exist. We also construct new $40$ inequivalent extremal doubly even self-dual $
Anev, Damyan +2 more
core +5 more sources
Construction for both self-dual codes and LCD codes [PDF]
Advances in Mathematics of Communications, 2021 From a given [n, k] code C, we give a method for constructing many [n, k] codes C' such that the hull dimensions of C and C' are identical. This method can be applied to constructions of both self-dual codes and linear complementary dual codes (LCD codes
Keita Ishizuka, Ken Saito
semanticscholar +1 more source
On Symbol-Triple Distance of a Class of Constacyclic Codes of Length 3
IEEE Access, 2023 Let $p\not =3$ be any prime. In this paper, we completely determine symbol-triple distance of all $\gamma $ -constacyclic codes of length $3p^{s}$ over the finite commutative chain ring ${\mathcal{ R}}=\mathbb F_{p^{m}}+u\mathbb F_{p^{m}}$ , where
Hai Q. Dinh +3 more
doaj +1 more source
Some New Quantum BCH Codes over Finite Fields
Entropy, 2021 Quantum error correcting codes (QECCs) play an important role in preventing quantum information decoherence. Good quantum stabilizer codes were constructed by classical error correcting codes.
Lijuan Xing, Zhuo Li
doaj +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
Constructing self-dual codes from group rings and reverse circulant matrices
Advances in Mathematics of Communications, 2021 In this work, we describe a construction for self-dual codes in which we employ group rings and reverse circulant matrices. By applying the construction directly over different alphabets, and by employing the well known extension and neighbor methods we ...
J. Gildea, A. Korban, A. Kaya, B. Yildiz
semanticscholar +1 more source
Construction of MDS Euclidean Self-Dual Codes via Two Subsets [PDF]
IEEE Transactions on Information Theory, 2020 The parameters of a $q$ -ary MDS Euclidean self-dual codes are completely determined by its length and the construction of MDS Euclidean self-dual codes with new length has been widely investigated in recent years.
Weijun Fang, Shutao Xia, Fang-Wei Fu
semanticscholar +1 more source