Results 11 to 20 of about 281 (29)
Constacyclic codes over 𝔽q𝒮𝒯 and their applications
AKCE International Journal of Graphs and CombinatoricsLet [Formula: see text], where p is an odd prime and r is a positive integer. Consider a ring [Formula: see text], where [Formula: see text] with [Formula: see text] and [Formula: see text] with [Formula: see text].
Amal S. Alali +3 more
doaj +1 more source
On reversibility problem in DNA bases over a class of rings
Applied Mathematics in Science and EngineeringLet [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].
Amal S. Alali +4 more
doaj +1 more source
On the Decoding Complexity of Cyclic Codes Up to the BCH Bound
, 2011 The standard algebraic decoding algorithm of cyclic codes $[n,k,d]$ up to the BCH bound $t$ is very efficient and practical for relatively small $n$ while it becomes unpractical for large $n$ as its computational complexity is $O(nt)$.
Elia, Michele +2 more
core +1 more source
Linear Skew Cyclic Codes over 𝔽qS
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria MatematicaIn this study, we focus on skew cyclic codes over the family of rings 𝔽q S where q is a power of a prime number and S = 𝔽q + v𝔽q with v2 = v. Structural properties of these codes are studied in detail. Obtained results lead us to characterize 𝔽q S-linear
Yildirim Tulay
doaj +1 more source
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria MatematicaLet S = ℤp[u, v]/〈u2, v2, uv − uv〉 be a semi-local ring, where p is a prime number. In the present article, we determine the generating sets of S and use them to construct the structures of ℤpS-additive cyclic and constacyclic codes.
Ashraf Mohammad +3 more
doaj +1 more source
Applications of some special numbers obtained from a difference equation of degree three
, 2017 In this paper we present applications of some special numbers obtained from a difference equation of degree three, especially in the Coding Theory. As a particular case, we obtain the generalized Pell-Fibonacci-Lucas numbers, which were extended to the ...
Flaut, Cristina, Savin, Diana
core +1 more source
Minimal Codewords in Linear Codes [PDF]
, 2004 2000 Mathematics Subject Classification: 94B05, 94B15.Cyclic binary codes C of block length n = 2^m − 1 and generator polynomial g(x) = m1(x)m2^s+1(x), (s, m) = 1, are considered. The cardinalities of the sets of minimal codewords of weights 10 and 11 in
Borissov, Yuri, Manev, Nickolai
core
Skew cyclic codes over 𝔻4R and their applications to DNA codes construction
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria MatematicaThe fundamental aim of this research is to analyze the configuration of 𝔽4R submodules, skew cyclic codes over 𝔽4R and establish their connection with DNA codes, where 𝔽4 is a field of order 4 and R = 𝔽4 + u𝔽4 + v𝔽4 + w𝔽4 with u2 = u, v2 = v, w2 = w, uv =
Rehman Nadeem ur +2 more
doaj +1 more source
Two-dimensional cyclic codes over a finite chain ring
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria MatematicaIn this paper, we have determined the generators and rank of a 2D cyclic code of length mn over a finite chain ring ℛ with residue field 𝔽q, where m is arbitrary and q ≡ 1(mod n).
Garg Disha, Dutt Sucheta
doaj +1 more source
A linear construction for certain Kerdock and Preparata codes
, 1993 The Nordstrom-Robinson, Kerdock, and (slightly modified) Pre\- parata codes are shown to be linear over $\ZZ_4$, the integers $\bmod~4$. The Kerdock and Preparata codes are duals over $\ZZ_4$, and the Nordstrom-Robinson code is self-dual. All these codes
A. R. Calderbank +5 more
core +1 more source