Cyclic codes and self-dual codes over F/sub 2/+uF/sub 2/
From MaRDI portal
Publication:4701378
DOI10.1109/18.761278zbMath0958.94025OpenAlexW2042187478MaRDI QIDQ4701378
Parampalli Udaya, Alexis Bonnecaze
Publication date: 21 November 1999
Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1109/18.761278
Related Items (only showing first 100 items - show all)
On cyclic codes over \(\mathbb{Z}_q [u / \langle u^2 \rangle\) and their enumeration] ⋮ Repeated-root constacyclic codes of prime power length over \(\frac{\mathbb{F}_{p^m} [u}{\langle u^a \rangle}\) and their duals] ⋮ Construction of LCD and new quantum codes from cyclic codes over a finite non-chain ring ⋮ (1 + u) constacyclic and cyclic codes over \(F_{2} + uF_{2}\) ⋮ On cyclic DNA codes over \({\mathbb {F}}_2+u{\mathbb {F}}_2\) ⋮ On the ℤq-Simplex codes and its weight distribution for dimension 2 ⋮ RT distances and Hamming distances of constacyclic codes of length \(8p^s\) over \(\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}\) ⋮ Cyclic and constacyclic codes over a non-chain ring ⋮ On the structure of cyclic codes over the ring \(\mathbb{Z}_{2^s} [u/\langle u^k \rangle\)] ⋮ Negacyclic codes over the local ring \(\mathbb{Z}_4 [v / \langle v^2 + 2 v \rangle\) of oddly even length and their gray images] ⋮ ℤ2(ℤ2 + uℤ2)-Additive cyclic codes and their duals ⋮ The homogeneous distance of \((1+u^2)\)-constacyclic codes over \(\mathbb{F}_2[u/\langle u^3\rangle\) and its applications] ⋮ Cyclic codes over \(\mathbb{F}_{2^m}[u/\langle u^k\rangle \) of oddly even length] ⋮ Cyclic codes over the rings \(\mathbb Z_2 + u\mathbb Z_2\) and \(\mathbb Z_2 + u\mathbb Z_2 + u^2 \mathbb Z_2\) ⋮ Cyclic DNA codes over the ring \(\mathbb {F}_2+u\mathbb {F}_2+v\mathbb {F}_2+uv\mathbb {F}_2+v^2\mathbb {F}_2+uv^2\mathbb {F}_2\) ⋮ DFT for cyclic code over \(F_p+ uF_p+\cdots+ u^{k-1}F_p\) ⋮ On ℤq-linear and ℤq-Simplex codes and its related parameters forqis a prime power ⋮ Constacyclic codes of length \(8p^s\) over \(\mathbb{F}_{p^m} + u\mathbb{F}_{p^m}\) ⋮ A family of constacyclic codes over \(\mathbb F_{2} + u\mathbb F_{2} + v\mathbb F_{2} + uv\mathbb F_{2}\) ⋮ Unnamed Item ⋮ Design of new \(4\times 4\) S-box from finite commutative chain rings ⋮ Ideal structure of Zq + uZq and Zq + uZq-cyclic codes ⋮ On \(\mathbb{F}_2 RS\)-cyclic codes and their applications in constructing optimal codes ⋮ An explicit expression for Euclidean self-dual cyclic codes over \(\mathbb{F}_{2^m} + u \mathbb{F}_{2^m}\) of length \(2^s\) ⋮ Cyclic codes over \(M_{2}(\mathbb {F}_{2}+u\mathbb {F}_{2})\) ⋮ Complete classification of \((\delta + \alpha u^2)\)-constacyclic codes over \(\mathbb{F}_{2^m} [u/\langle u^4 \rangle\) of oddly even length] ⋮ An efficient method to construct self-dual cyclic codes of length \(p^s\) over \(\mathbb{F}_{p^m} + u \mathbb{F}_{p^m} \) ⋮ Constacyclic codes of length \(p^s\) over \(\mathbb F_{p^m} + u\mathbb F_{p^m}\) ⋮ Cyclic DNA codes over \(\mathbb{F}_2+u\mathbb{F}_2+v\mathbb{F}_2+uv\mathbb{F}_2\) and their applications ⋮ Structure of codes over the ring \(Z_3[v/\langle v^3 - v\rangle\)] ⋮ Unnamed Item ⋮ On Reed-Muller codes over \(\mathbb F_2+u\mathbb F_2\) and some applications ⋮ On self-dual constacyclic codes of length \(p^s\) over \(\mathbb{F}_{p^m} + u \mathbb{F}_{p^m}\) ⋮ Linear codes over \(\mathbb{F}_q\times (\mathbb{F}_q+v\mathbb{F}_q)\) ⋮ Constructing quasi-cyclic codes from linear algebra theory ⋮ An explicit representation and enumeration for self-dual cyclic codes over \(\mathbb{F}_{2^m}+u\mathbb{F}_{2^m}\) of length \(2^s\) ⋮ Cyclic and LCD Codes over a Finite Commutative Semi-local Ring ⋮ Constacyclic codes of length \(2p^{s}\) over \(\mathbb{F}_{p^m} + u \mathbb{F}_{p^m}\) ⋮ Cyclic codes over a non-commutative finite chain ring ⋮ Negacyclic codes of length \(4 p^s\) over \(\mathbb{F}_{p^m} + u \mathbb{F}_{p^m}\) and their duals ⋮ Cyclic codes over \({\mathbb{F}}_2 + u{\mathbb{F}}_2 + v{\mathbb{F}}_2 + uv{\mathbb{F}}_2\) ⋮ Skew constacyclic codes over finite commutative semi-simple rings ⋮ Cyclic codes over \(R = F_p + uF_p + \cdots + u^{k - 1}F_p\) with length \(p^sn\) ⋮ \((1 + v)\)-constacyclic codes over \(\mathbb F_2 + u\mathbb F_2 + v\mathbb F_2 + uv\mathbb F_2\) ⋮ Weight distributions of generalized quasi-cyclic codes over \(\mathbb{F}_q + u \mathbb{F}_q\) ⋮ Construction of cyclic codes over \(\mathbb F_2 + u\mathbb F_2\) for DNA computing ⋮ On a class of constacyclic codes of length 4ps over 𝔽pm + u𝔽pm ⋮ On (α + uβ)-constacyclic codes of length 4ps over 𝔽pm + u𝔽pm∗ ⋮ Cyclic codes over R3,m ⋮ \((1+\lambda u)\)-constacyclic codes over \(\mathbb F_{p}[u/\langle u^m\rangle\)] ⋮ Cyclic codes over \(M_2(\mathbb F_2)\) ⋮ Negacyclic codes of length \(2p^s\) over \(\mathbb{F}_{p^m} + u \mathbb{F}_{p^m}\) ⋮ Type I and Type II codes over the ring 𝔽2 + u𝔽2 + v𝔽2 + uv𝔽2 ⋮ Cyclic codes over $\mathbb{Z}_{4}+u\mathbb{Z}_{4}+u^{2}\mathbb{Z}_{4}$ ⋮ Cyclic codes over \(R_{k}\) ⋮ On cyclic codes over the ring \(\mathbb Z_p[u/\langle u^k\rangle\)] ⋮ DNA cyclic codes over the ring 𝔽2[u,v/〈u2 − 1,v3 − v,uv − vu〉] ⋮ Lee distance of cyclic and \((1 + u\gamma)\)-constacyclic codes of length \(2^s\) over \(\mathbb{F}_{2^m} + u \mathbb{F}_{2^m} \) ⋮ On self-duality and hulls of cyclic codes over \(\frac{\mathbb{F}_{2^m}[u}{\langle u^k\rangle}\) with oddly even length] ⋮ Optimal binary codes from trace codes over a non-chain ring ⋮ Primitive idempotents of irreducible cyclic codes and self-dual cyclic codes over Galois rings ⋮ On constacyclic codes of length \(4p^s\) over \(\mathbb{F}_{p^m} +u\mathbb{F}_{p^m}\) ⋮ QUATERNARY CONSTRUCTION OF QUANTUM CODES FROM CYCLIC CODES OVER $\mathbb{F}_4 + u\mathbb{F}_4$ ⋮ Cyclic codes over local Frobenius rings of order 16 ⋮ Complete classification of \((\delta +\alpha u^2)\)-constacyclic codes over \(\mathbb {F}_{3^m}[u/\langle u^4\rangle \) of length \(3n\)] ⋮ Cyclic codes over the ring \(F_2+uF_2+vF_2\) ⋮ Cyclic codes of odd length over \(\mathbb{Z}_4 [u/u^k\)] ⋮ Two and three weight codes over \(\mathbb {F}_p+u\mathbb {F}_p\) ⋮ Classification of self-dual cyclic codes over the chain ring \(\mathbb Z_p[u/\langle u^3 \rangle \)] ⋮ RT distance and weight distributions of Type 1 constacyclic codes of length 4ps over Fpm[u] ⋮ Linear codes over \({\mathbb F}_{q}[u/(u^s)\) with respect to the Rosenbloom-Tsfasman metric] ⋮ Constacyclic codes over \(\mathbb F_2 + u\mathbb F_2\) ⋮ Constacyclic codes of length \(np^s\) over \(\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}\) ⋮ Cyclic codes over the ring \(\mathrm{GR}(p^e, m) [u / \langle u^k \rangle \)] ⋮ Self-dual cyclic and quantum codes over ℤ2 × (ℤ2 + uℤ2) ⋮ A note on cyclic codes over ℤ4 + uℤ4 ⋮ Skew constacyclic codes over finite fields and finite chain rings ⋮ Construction and enumeration for self-dual cyclic codes of even length over \(\mathbb{F}_{2^m} + u \mathbb{F}_{2^m} \) ⋮ DNA computing over the ring ℤ4[v/〈v2 − v〉] ⋮ Cyclic codes over a non-chain ring \(R_{e,q}\) and their application to LCD codes ⋮ Unnamed Item ⋮ On self-orthogonal group ring codes ⋮ Type I and type II codes over the ring \(\mathbb{F}_2+s \mathbb{F}_2+s^2\mathbb{F}_2\) ⋮ A class of constacyclic codes and skew constacyclic codes over \(\mathbb{Z}_{2^s}+u\mathbb{Z}_{2^s}\) and their Gray images ⋮ Cyclic codes over \(\mathbb{Z}_{4}\) of oddly even length. ⋮ Cyclic DNA codes over the ring $\mathbb{Z}_4+u\mathbb{Z}_4+u^2\mathbb{Z}_4$ ⋮ Self-orthogonal codes over \(\mathbb{Z}_4\) arising from the chain ring \(\mathbb{Z}_4 [u / \langle u^2 + 1 \rangle \)] ⋮ Cyclic codes over \(\mathcal M_4(\mathbb F_2)\) ⋮ The dual code of any \((\delta + \alpha u^2)\)-constacyclic code over \(\mathbb{F}_{2^m} [u \slash \langle u^4 \rangle\) of oddly even length] ⋮ REPEATED-ROOT CONSTACYCLIC CODES OVER F3+uF3+uvF3 ⋮ Unnamed Item ⋮ Classification of cyclic codes over a non-Galois chain ring \(\mathbb{Z}_p [u / \langle u^3 \rangle\)] ⋮ Repeated root constacyclic codes of length mps over 𝔽pr + u𝔽pr + ⋯ + ue-1𝔽pr ⋮ Decoding of cyclic codes over the ring \(\frac{F_2[u}{{\langle{u^t}\rangle }}\)] ⋮ Cyclic codes over \(M_4 (\mathbb{F}_2+u\mathbb{F}_2)\) ⋮ $(1-2u^2)$-constacyclic codes over $\mathbb{F}_p+u\mathbb{F}_p+u^2\mathbb{F}_p$ ⋮ Explicit constructions of cyclic and negacyclic codes of length 3ps over 𝔽pm + u𝔽pm ⋮ On quantum codes obtained from cyclic codes over 𝔽2 + u𝔽2 + u2𝔽2 ⋮ Self-dual codes over ℤ4 + wℤ4 ⋮ Cyclic codes over the ring \(\mathbb{Z}_p [u, v / \langle u^2, v^2, u v - v u \rangle\)]
This page was built for publication: Cyclic codes and self-dual codes over F/sub 2/+uF/sub 2/