Two dimensional constacyclic codes of arbitrary length over finite fields

2021 ◽  
Author(s):  
Swati Bhardwaj ◽  
Madhu Raka
Keyword(s):  
Finite Fields ◽  
Two Dimensional ◽  
Constacyclic Codes ◽  
Arbitrary Length

Constructing MDS Galois self-dual constacyclic codes over finite fields

2021 ◽  
Vol 344 (6) ◽  
pp. 112388
Author(s):  
Jiafu Mi ◽  
Xiwang Cao
Keyword(s):  
Finite Fields ◽  
Constacyclic Codes

MDS Constacyclic Codes of Prime Power Lengths Over Finite Fields and Construction of Quantum MDS Codes

2020 ◽  
Vol 59 (10) ◽  
pp. 3043-3078
Author(s):  
Hai Q. Dinh ◽  
Ramy Taki ElDin ◽  
Bac T. Nguyen ◽  
Roengchai Tansuchat
Keyword(s):  
Finite Fields ◽  
Prime Power ◽  
Mds Codes ◽  
Constacyclic Codes ◽  
Quantum Mds Codes

A Note on Skew Cyclic Codes over a Class of Rings

2020 ◽  
Vol 27 (04) ◽  
pp. 703-712
Author(s):  
Hai Q. Dinh ◽  
Bac T. Nguyen ◽  
Songsak Sriboonchitta
Keyword(s):  
Finite Field ◽  
Cyclic Code ◽  
Cyclic Codes ◽  
General Setting ◽  
Constacyclic Codes ◽  
Arbitrary Length ◽  
Skew Cyclic Codes

We study skew cyclic codes over a class of rings [Formula: see text], where each [Formula: see text] [Formula: see text] is a finite field. We prove that a skew cyclic code of arbitrary length over R is equivalent to either a usual cyclic code or a quasi-cyclic code over R. Moreover, we discuss possible extension of our results in the more general setting of [Formula: see text]-dual skew constacyclic codes over R, where δR is an automorphism of R.

scholarly journals The average dimension of the Hermitian hull of constacyclic codes over finite fields of square order

2018 ◽  
Vol 12 (3) ◽  
pp. 451-463 ◽  
Author(s):  
Somphong Jitman ◽  
◽  
Ekkasit Sangwisut ◽  
Keyword(s):  
Finite Fields ◽  
Constacyclic Codes ◽  
Average Dimension

Three-dimensional and multicellular steady and unsteady convection in fluid-saturated porous media at high Rayleigh numbers

1979 ◽  
Vol 94 (1) ◽  
pp. 25-38 ◽  
Author(s):  
Gerald Schubert ◽  
Joe M. Straus
Keyword(s):  
Single Cell ◽  
Cross Section ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Arbitrary Length ◽  
Dimensional Flow ◽  
A Value ◽  
Square Cylinders ◽  
Two Dimensional Flow ◽  
Rayleigh Numbers

In an effort to determine the characteristics of the various types of convection that can occur in a fluid-saturated porous medium heated from below, a Galerkin approach is used to investigate three-dimensional convection in a cube and two-dimensional convection in a square cross-section. Strictly two-dimensional, single-cell flow in a square cross-section is steady for Rayleigh numbers R between 4π2 and a critical value which lies between 300 and 320; it is unsteady at higher values of R. Double-cell, two-dimensional flow in a square cross-section becomes unsteady when R exceeds a value between 650 and 700, and triple-cell motion is unsteady for R larger than a value between 800 and 1000. Considerable caution must be exercised in attributing physical reality to these flows. Strictly two-dimensional, steady, multicellular convection may not be realizable in a three-dimensional geometry because of instability to perturbations in the orthogonal dimension. For example, even though single-cell, two-dimensional convection in a square cross-section is steady at R = 200, it cannot exist in either an infinitely long square cylinder or in a cube. It could exist, however, in a cylinder whose length is smaller than 0.38 times the dimension of its square cross-section. Three-dimensional convection in a cube becomes unsteady when R exceeds a value between 300 and 320, similar to the unicellular two-dimensional flow in a square cross-section. Nusselt numbers Nu, generally accurate to 1%, are given for the strictly two-dimensional flows up to R = 1000 and for three-dimensional convection in cubes up to R = 500. Single-cell, two-dimensional, steady convection in a square cross-section transports the most heat for R < 97; this mode of convection is also stable in square cylinders of arbitrary length including the cube for R < 97. Steady three-dimensional convection in cubes transports more heat for 97 [lsim ] R [lsim ] 300 than do any of the realizable two-dimensional modes. At R [gsim ] 300 the unsteady modes of convection in both square cylinders and cubes involve wide variations in Nu.

scholarly journals Skew Constacyclic Codes over Finite Fields and Finite Chain Rings

2016 ◽  
Vol 2016 ◽  
pp. 1-17 ◽  
Author(s):  
Hai Q. Dinh ◽  
Bac T. Nguyen ◽  
Songsak Sriboonchitta
Keyword(s):  
Finite Fields ◽  
Bch Codes ◽  
Constacyclic Codes ◽  
Finite Chain ◽  
Dual Codes ◽  
Negacyclic Codes ◽  
Finite Chain Rings

This paper overviews the study of skewΘ-λ-constacyclic codes over finite fields and finite commutative chain rings. The structure of skewΘ-λ-constacyclic codes and their duals are provided. Among other results, we also consider the Euclidean and Hermitian dual codes of skewΘ-cyclic and skewΘ-negacyclic codes over finite chain rings in general and overFpm+uFpmin particular. Moreover, general decoding procedure for decoding skew BCH codes with designed distance and an algorithm for decoding skew BCH codes are discussed.

On constacyclic codes over finite fields

2015 ◽  
Vol 8 (4) ◽  
pp. 617-636 ◽  
Author(s):  
Anuradha Sharma ◽  
Saroj Rani
Keyword(s):  
Finite Fields ◽  
Constacyclic Codes

scholarly journals Constacyclic Codes of Arbitrary Length over Fq+uFq+⋯+ue−1Fq

2019 ◽  
Vol 6 (1) ◽  
pp. 67-84
Author(s):  
Marziyeh Beygi ◽  
Shohreh Namazi ◽  
Habib Sharif
Keyword(s):  
Constacyclic Codes ◽  
Arbitrary Length

scholarly journals Constacyclic Codes over Finite Chain Rings of Characteristic p

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 303
Author(s):  
Sami Alabiad ◽  
Yousef Alkhamees
Keyword(s):  
Local Rings ◽  
Constacyclic Codes ◽  
Finite Chain ◽  
Dual Codes ◽  
Chain Ring ◽  
Characteristic P ◽  
Arbitrary Length ◽  
Cyclotomic Cosets ◽  
Finite Chain Rings ◽  
Polynomial Representations

Let R be a finite commutative chain ring of characteristic p with invariants p,r, and k. In this paper, we study λ-constacyclic codes of an arbitrary length N over R, where λ is a unit of R. We first reduce this to investigate constacyclic codes of length ps (N=n1ps,p∤n1) over a certain finite chain ring CR(uk,rb) of characteristic p, which is an extension of R. Then we use discrete Fourier transform (DFT) to construct an isomorphism γ between R[x]/<xN−λ> and a direct sum ⊕b∈IS(rb) of certain local rings, where I is the complete set of representatives of p-cyclotomic cosets modulo n1. By this isomorphism, all codes over R and their dual codes are obtained from the ideals of S(rb). In addition, we determine explicitly the inverse of γ so that the unique polynomial representations of λ-constacyclic codes may be calculated. Finally, for k=2 the exact number of such codes is provided.

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