Results 1 to 10 of about 301 (47)

On reversibility problem in DNA bases over a class of rings

Applied Mathematics in Science and Engineering
Let [Formula: see text] be a non-chain ring of characteristic 4, where [Formula: see text] and [Formula: see text]. In this article, we discuss reversible cyclic codes of odd lengths over the ring [Formula: see text].
Mohd Asim, Ghulam Mohammad, Mohammad Ashraf   +2 more
exaly   +3 more sources

Non-binary quantum codes from constacyclic codes over 𝔽q[u1, u2,…,uk]/⟨ui3 = ui, uiuj = ujui⟩

Open Mathematics, 2022
Let q=pmq={p}^{m}, pp be an odd prime, and Rk=Fq[u1,u2,…,uk]/⟨ui3=ui,uiuj=ujui⟩{R}_{k}={{\mathbb{F}}}_{q}\left[{u}_{1},{u}_{2},\ldots ,{u}_{k}]\hspace{-0.08em}\text{/}\hspace{-0.08em}\langle {u}_{i}^{3}={u}_{i},{u}_{i}{u}_{j}={u}_{j}{u}_{i}\rangle ...
Kong Bo, Zheng Xiying
doaj   +1 more source

DNA codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022
A one to one correspondence between the elements of a finite local Frobenius non-chain ring of length 5 and nilpotency index 4, and k-tuples of DNA codewords is established.
Castillo-Guillén C. A., Álvarez-García C.   +1 more
doaj   +1 more source

Construction of reversible cyclic codes over 𝔽q + u𝔽q + u2𝔽q

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023
Let q be a power of prime p. In this article, we investigate the reversible cyclic codes of arbitrary length n over the ring R = 𝔽q +u𝔽q + u2𝔽q, where u3 = 0 mod q.
Rehman Nadeem ur, Ahmad Mohammad Fareed, Azmi Mohd   +2 more
doaj   +1 more source

Self-Dual Cyclic Codes Over M2(ℤ4)

Discussiones Mathematicae - General Algebra and Applications, 2022
In this paper, we study the structure of cyclic codes overM2(ℤ4) (the matrix ring of matrices of order 2 over ℤ4), which is perhaps the first time that the ring is considered as a code alphabet.
Bhowmick Sanjit, Pal Joydeb, Bandi Ramakrishna, Bagchi Satya   +3 more
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

Skew Cyclic codes over $\F_q+u\F_q+v\F_q+uv\F_q$ [PDF]

, 2015
In this paper, we study skew cyclic codes over the ring $R=\F_q+u\F_q+v\F_q+uv\F_q$, where $u^{2}=u,v^{2}=v,uv=vu$, $q=p^{m}$ and $p$ is an odd prime. We investigate the structural properties of skew cyclic codes over $R$ through a decomposition theorem.
Shi, Minjia, Solé, Patrick, Yao, Ting
core   +4 more sources

Monomial codes seen as invariant subspaces

Open Mathematics, 2017
It is well known that cyclic codes are very useful because of their applications, since they are not computationally expensive and encoding can be easily implemented. The relationship between cyclic codes and invariant subspaces is also well known.
García-Planas María Isabel, Magret Maria Dolors, Um Laurence Emilie   +2 more
doaj   +1 more source

Polynomial evaluation over finite fields: new algorithms and complexity bounds [PDF]

, 2011
An efficient evaluation method is described for polynomials in finite fields. Its complexity is shown to be lower than that of standard techniques when the degree of the polynomial is large enough. Applications to the syndrome computation in the decoding
A. Borodin, D.E. Knuth, D.V. Sarwate, Davide Schipani, E. Costa, F.J. MacWilliams, Joachim Rosenthal, M. Elia, M. Paterson, Michele Elia, R. Lidl, R.E. Blahut, S. Winograd, V.Y. Pan   +13 more
core   +1 more source

Constacyclic codes over 𝔽pm[u1, u2,⋯,uk]/〈 ui2 = ui, uiuj = ujui〉

Open Mathematics, 2018
In this paper, we study linear codes over ring Rk = 𝔽pm[u1, u2,⋯,uk]/〈ui2$\begin{array}{} u^{2}_{i} \end{array} $ = ui, uiuj = ujui〉 where k ≥ 1 and 1 ≤ i, j ≤ k.
Zheng Xiying, Kong Bo
doaj   +1 more source