Ternary cyclic codes

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August undefined, 2024

Web31 Mar 2024 · It follows that a cyclic code is an ideal in the quotient ring Fqrxs{xxn ´ 1y which is a principal ideal ring. Hence any cyclic code C can be viewed as a principal ideal … WebA table is given containing all ternary cyclic codes of length less than 40 and having a minimum distance exceeding the BCH bound. lt seems that almost all lower bounds are …

On the Construction of Quantum and LCD Codes from Cyclic …

WebIn this paper, we present two classes of new optimal ternary cyclic codes C ( 2, v) by using monomials x2 and xv for some suitable v and explain the novelty of the codes. … WebArchitectures with 6-Input LUTs in Adaptive Logic Modules. In Intel FPGA device families with 6-input LUT in their basic logic structure, ALMs can simultaneously add three bits. … lake district mighty hike route

Further results on optimal ternary cyclic codes - ScienceDirect

WebCyclic redundancy check (CRC) aided polar code with successive cancellation list (SCL) decoder and 4-PSK. LDPC code with 4-PSK. ... Interestingly, the ternary polar code with the binary CRC and the converter performs slightly better than the ternary polar code with the … Web24 Jan 2024 · In this paper, we settle an open problem about a class of optimal ternary cyclic codes which was proposed by Ding and Helleseth. Let C_ (1,e) be a cyclic code of … Webfamilies of ternary cyclic codes with length n=3m−1for odd mand dimension k∈ {n/2,(n+2)/2} whose minimum distances have a square-root-likelower bound. Their duals have … lake district motorcycle routes

Four inﬁnite families of ternary cyclic codes with a square-root …

A family of optimal ternary cyclic codes with minimum ... - Springer

Web1 Mar 2024 · In this paper, the two families of optimal ternary cyclic codes with parameters of [ 3 m − 1 , 3 m − 1 − 2 m , 4 ] are presented. Some conclusions proposed by Wang and … Web13 Mar 2016 · Give a complete list of ternary cyclic code of length 3. For x 3 − 1 ∈ F 3 [ x], x 3 − 1 = ( x − 1) ( x 2 + x + 1). Generator polynomials of ternary code of length 3 are { 1, x − 1, … helicon microwaveWebThe KWIC (keyword-in-context) index is produced by cyclic permutation of significant words in the title of the publication. The text covers materials in rock mechanics and … helicon missionary baptist church grady al

"WebI am a Sr. Member of IEEE and ACM, IEEE Computer Society Distinguished Visitor (2024-2024), Distinguished Speaker of ACM (2024-2024) and Vice President of Society for Data … " - Ternary cyclic codes

Ternary cyclic codes

Algebraic Decoding of Some Quadratic Residue Codes …

Web1 Jan 2024 · one to get optimal ternary cyclic codes simply by choosing appropriate integers m, s and t . Furthermore, these facts can simplify the proof of the novelt y of the …

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WebIn this paper, an explicit expression of the weak-locator polynomial for p-ary quadratic residue codes is presented by a modification of the Feng-Tzeng matrix method. The … Webgroup of C is a subgroup of the cyclic group of order 8. In this talk, we report on the existence of a regular Hadamard matrix ... On extremal self-dual ternary codes of lengths …

Web5 Apr 2024 · You can use optional chaining when attempting to call a method which may not exist. This can be helpful, for example, when using an API in which a method might be … WebCyclic codes as a subclass of linear codes have wide applications in communication systems, consumer electronics and data storage systems, due to their efficient encoding …

WebIMP: Verify that you have received the question paper with the correct course, code, branch etc. 1. This Question paper comprises of three Sections -A, B, & C. It consists of Multiple … WebPublished: November 2024. Abstract. Let C ( u, v) denote the ternary cyclic code with two zeros αu and αv, where α is a generator of F ∗ 3m and 1 ≤ u, v ≤ 3m − 1. In this paper, we …

WebCyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and …

WebTwo classes of new optimal ternary cyclic codes over finite fields are presented by using monomials and the weight distribution of these codes is determined. Due to their wide … lake district memphis tnWebternary cyclic codes by determining the solutions of certain equations over F3m. Especially, by setting u = 3m−1 2 and properly choosing integers v, several classes of … helicon nftWeb1 Jun 2015 · 1 Answer. Sorted by: 0. Hint: Over the field G F ( 3) we have. p ( x) = x 27 − 1 = ( x − 1) 27. by the so called freshman's dream (check this if you don't see it right away). … helicon missionary baptist churchWebminium distance of a cyclic code, based on investigation of the defining set. Some new theorems are derived. These and earlier techniques are applied to find lower bounds for … lake district motorway farm shopWeb1 Oct 2024 · In 2013, new classes of optimal ternary cyclic codes C 3 (1, v) and nine problems were presented by using monomials x v over F 3 m [13]. After that, many … lake district map of fellsWeb24 Jan 2024 · However, compared with the extensive study of cyclic codes, negacyclic codes are much less studied. In this paper, several families of ternary negacyclic codes … lake district met office weather forecastWeb10 Apr 2024 · In 2015, from the cyclic codes over F q + v F q + v 2 F q + v 3 F q (where q = p m, p is a prime such that 3 (p − 1), v 4 = v, and m is a positive integer), Gao et al. constructed new quantum codes over F q. Afterwards, Ozen et al. constructed many ternary quantum codes from cyclic codes over F 3 + u F 3 + v F 3 + u v F 3. lake district mountain accidents