Results 1 to 10 of about 529,213 (275)

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]

Entropy
Quasi-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

Self-Dual Codes [PDF]

, 2002
Self-dual codes are important because many of the best codes known are of this type and they have a rich mathematical theory. Topics covered in this survey include codes over F_2, F_3, F_4, F_q, Z_4, Z_m, shadow codes, weight enumerators, Gleason-Pierce ...
Rains, E. M., Sloane, N. J. A.
core   +3 more sources

Symplectic QSD, LCD, and ACD Codes over a Non-Commutative Non-Unitary Ring of Order Nine [PDF]

Entropy
We 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, Patrick Solé, Adel Alahmadi, Widyan Basaffar   +3 more
doaj   +2 more sources

Dual-Message QR Codes

Sensors
A novel dual-message QR code is proposed for carrying two individual messages that can be read by standard QR code readers: one from a close range and the other from a large distance.
Kuo-Chien Chou, Ran-Zan Wang
doaj   +3 more sources

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

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, Bac T. Nguyen, Hiep T. Luu, Woraphon Yamaka   +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

Self dual, reversible and complementary duals constacyclic codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4.

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., Álvarez-García C.   +1 more
doaj   +1 more source

Self-Dual Codes, Symmetric Matrices, and Eigenvectors

IEEE Access, 2021
We introduce a consistent and efficient method to construct self-dual codes over $GF(q)$ using symmetric matrices and eigenvectors from a self-dual code over $GF(q)$ of smaller length where $q \equiv 1 \pmod 4$ . Using this method, which is called a
Jon-Lark Kim, Whan-Hyuk Choi
doaj   +1 more source

Extremal Binary and Ternary Codes of Length 60 with an Automorphism of Order 29 and a Generalization

Mathematics, 2022
In this paper, all extremal Type I and Type III codes of length 60 with an automorphism of order 29 are classified up to equivalence. In both cases, it has been proven that there are three inequivalent codes.
Stefka Bouyuklieva, Javier de la Cruz, Darwin Villar   +2 more
doaj   +1 more source