Some results on triple cyclic codes over z4

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August undefined, 2024

WebKeywords: cyclic codes, codes over rings AMS Classiﬁcation: 94B15 1. Introduction Cyclic codes are an important class of codes from both a theoretical and a practical viewpoint. … WebUndergraduate computer science students need at learn and use the mathematical method of abstraction, explanation, and pr...

Construction of cyclic DNA codes over the ring Z4[u]/〈u2−1

WebJan 13, 2024 · In this paper, we obtain generating set of polynomials of two-dimensional cyclic codes over the ring R=Z4[u]/(u2-1), where u2=1. Moreover, we find generator … WebLet r,s,t be three positive integers and C be a binary linear code of lenght r+s+t. We say that C is a triple cyclic code of lenght (r,s,t) over Z2 if the set of coordinates can be partitioned … imuoto high life

[PDF] On double cyclic codes over Z4 Semantic Scholar

WebPreviously, (linear) codes over Z/sub 4/ and quasi-cyclic (QC) codes (over fields) have been shown to yield useful results in coding theory. Combining these two ideas we study Z/sub … WebFeb 12, 2014 · In this paper, we study Z2Z4-additive cyclic codes. These codes are identified as Z4[x]-submodules of the ring Rr,s=Z2[x]/〈xr-1〉×Z4[x] ... We show that the duals of … WebSep 13, 2015 · In this paper, we study cyclic codes over the ring R = ℤ4 + uℤ4, u2 = 0. We discuss the Galois ring extensions of R and the ideal structure of these extensions. We … dutch fork middle school teachers

1-Generator quasi-cyclic and generalized quasi-cyclic codes over …

Quasi-cyclic codes over Z/sub 4/ and some new binary codes

WebSep 26, 2024 · T. Abualrub, I. Siap, Cyclic codes over the rings Z2 + uZ2 and Z2 + uZ2 + u2Z2, Des Codes Crypt 42 (2007) 273–287. T. Abualrub, I. Siap, Reversible cyclic codes … WebDOI: 10.1587/TRANSFUN.E99.A.998 Corpus ID: 26220569; Some Results on Triple Cyclic Codes over Z4 @article{Wu2016SomeRO, title={Some Results on Triple Cyclic Codes … imuny oneWebCROSS-REFERENCE TO RELATED APPLICATIONS. This patent application is a continuation of co-pending U.S. patent application Ser. No. 17/466,873, filed Sep. 3, 2024, which is a … imuons web solutions

"WebAnswer (1 of 3): Let’s make the problem more interesting; given m,n>0, determine whether \Z_m\oplus\Z_n is cyclic. Suppose the element ([a]_m,[b]_n) is a generator ... " - Some results on triple cyclic codes over z4

Some results on triple cyclic codes over z4

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WebA δθ-cyclic code is proved to be a left R[x,θ,δθ]-submodule of R[x,θ,δθ] hxn−1i. The form of a parity-check matrix of a free δθ-cyclic codes of even length n is presented. These codes … WebMar 6, 2024 · codes over R. Then, by deﬁning some Gray maps, we show that the images of (skew) (1,2u)-polycyclic codes over R are cyclic or quasi-cyclic with index 2 over Z4. …

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WebMar 15, 2015 · Q. Show that $\\mathbb{Z_3 x Z_4}$ is a cyclic group. So my question is there a faster way besides listing all the elements and besides knowing the theorem. … Webthe generators of triple cyclic codes and their duals. 1 Introduction Codes over nite rings have been studied since the early 1970s. Recently codes over rings have generated a lot …

WebAlgorithms for the minimal polynomial and the inverse of a level-n(r1, r2,…,rn)-block circulant matrix over any field are presented by means of the algorithm for the Gröbner basis for … WebFeb 20, 2024 · In the past five decades, a great deal of mathematical effort in coding theory has been devoted to the study of quasi-cyclic (QC) and generalized quasi-cyclic (GQC) …

WebA triple cyclic code of length (r, s, t) over R is a set that can be partitioned into three parts that any cyclic shift of the coordinates of the three parts leaves the code invariant. These … WebAug 9, 2015 · In this paper, we study the theory for constructing DNA cyclic codes of odd length over $\Z_4 [u]/\langle u^2 \rangle$ which play an important role in DNA computing. …

Web4-cyclic self-dual codes. Some of the ﬁrst examples, aside from the trivial self-dual code (2), are supplemented quadratic residue codes the theory of which is developed in [2]. The …

WebWe determine the structure of cyclic codes over Z 4 for arbitrary even length giving the generator polynomial for these codes. We determine the number of cyclic codes for a … imuons web solutions pvt. ltdWebA Z2-triple cyclic code of block length (r, s, t) is a binary code of length r + s +1 such that the code is partitioned into three parts of lengths r, s and t such that each part is invariant … dutch fork poly clevisWebGraph Theory Or Its Application, Second Edition [PDF] [3aduh0klqjgg]. INTRODUCTION TO CHART MODELSGraphs and DigraphsCommon Families of GraphsGraph Modelling ApplicationsWalks and DistancePat... dutch fork silver foxesWebMay 5, 2024 · Abstract: We construct a class of Z4-double cyclic codes generated by pairs of polynomials. Based on the probabilistic method, we prove the asymptotic properties of … dutch fork silver foxes baseballWebSep 17, 2013 · Document Document Title; US08537584B2: Latch-off of synchronous rectification for light load control Disclosed is a light load control circuit and the method … dutch fork tennisWebMay 1, 2016 · In this paper, following the approaches given in and , we investigate some algebraic structures of double cyclic codes over Z 4. Some good nonlinear binary codes … imur family medicalWebThe code C is called a triple cyclic code of length (r, s, t) over R if the set of its coordinates can be partitioned into three parts so that any cyclic shift of the coordinates of the three … imuquin® immune health supplement for cats