LCD codes from tridiagonal Toeplitz matrices

Date

2021-10-01

Author

Shi, Minjia
Özbudak, Ferruh
Xu, Li
Solé, Patrick

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

311
views

0
downloads

Double Toeplitz (DT) codes are codes with a generator matrix of the form (I,T) with T a Toeplitz matrix, that is to say constant on the diagonals parallel to the main. When T is tridiagonal and symmetric we determine its spectrum explicitly by using Dickson polynomials, and deduce from there conditions for the code to be LCD. Using a special concatenation process, we construct optimal or quasi-optimal examples of binary and ternary LCD codes from DT codes over extension fields.

Subject Keywords

LCD codes, Toeplitz matrices, Dickson polynomials

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85109170073&origin=inward
https://hdl.handle.net/11511/91353

Journal

Finite Fields and their Applications

DOI

https://doi.org/10.1016/j.ffa.2021.101892

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

A new concatenated type construction for LCD codes and isometry codes CARLET, Claude; Guneri, Cem; Özbudak, Ferruh; SOLÉ, Patrick (2018-03-01) We give a new concatenated type construction for linear codes with complementary dual (LCD) over small finite fields. In this construction, we need a special class of inner codes that we call isometry codes. Our construction generalizes a recent construction of Carlet et al. (2014-2016) and of Gtineri et al. (2016). In particular, it allows us to construct LCD codes with improved parameters directly.
Physical subspace identification for helicopters Avcıoğlu, Sevil; Kutay, Ali Türker; Department of Aerospace Engineering (2019) Subspace identification is a powerful tool due to its well-understood techniques based on linear algebra (orthogonal projections and intersections of subspaces) and numerical methods like QR and singular value decomposition. However, the state space model matrices which are obtained from conventional subspace identification algorithms are not necessarily associated with the physical states. This can be an important deficiency when physical parameter estimation is essential. This holds for the area of helico...
Improved Three-Way Split Formulas for Binary Polynomial and Toeplitz Matrix Vector Products Cenk, Murat; Hasan, M. Anwar (2013-07-01) In this paper, we consider three-way split formulas for binary polynomial multiplication and Toeplitz matrix vector product (TMVP). We first recall the best known three-way split formulas for polynomial multiplication: the formulas with six recursive multiplications given by Sunar in a 2006 IEEE Transactions on Computers paper and the formula with five recursive multiplications proposed by Bernstein at CRYPTO 2009. Second, we propose a new set of three-way split formulas for polynomial multiplication that a...
Belief propagation decoding of polar codes under factor graph permutations Peker, Ahmet Gökhan; Yücel, Melek Diker; Department of Electrical and Electronics Engineering (2018) Polar codes, introduced by Arıkan, are linear block codes that can achieve the capacity of symmetric binary-input discrete memoryless channels with low encoding and decoding complexity. Polar codes of block length N are constructed by channel polarization method, which consists of channel combining and splitting operations to obtain N polarized subchannels from N copies of binary-input discrete memoryless channels. As N grows, symmetric channel capacities of the polarized subchannels converge to either 0 or...
Parallel computation of the diagonal of the inverse of a sparse matrix Fasllija, Edona; Manguoğlu, Murat; Department of Computer Engineering (2017) We consider the parallel computation of the diagonal of the inverse of a large sparse matrix. This problem is critical in many applications such as quantum mechanics and uncertainty quantification, where a subset of the entries of the inverse matrix, usually the diagonal, is required. A straightforward approach involves inverting the matrix explicitly and extracting the diagonal of the computed inverse. This approach, however, almost always is too costly for large sparse matrices since the inverse is often ...

Citation Formats

M. Shi, F. Özbudak, L. Xu, and P. Solé, “LCD codes from tridiagonal Toeplitz matrices,” Finite Fields and their Applications, pp. 0–0, 2021, Accessed: 00, 2021. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85109170073&origin=inward.