Ternary cyclic codes

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August undefined, 2024

WebCyclic codes are an important subclass of linear codes and have wide applications in data storage systems, communi-cation systems and consumer electronics. In this paper, two … 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 …

Further results on optimal ternary cyclic codes

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 … WebHighly sensitive and efficient hydrazine sensor probe development based on MoO3/CuO/ZnO ternary mixed metal oxide nano‐composites for sustainable environment Md Abdus … headphones google assistant

On a conjecture about a class of optimal ternary cyclic codes

Webminium 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 … WebTernary), Reed Muller Codes, And Kerdock Codes.Bounds on Codes: Gilbert Bound, Upper Bound, Linear Programming Bounds, Hamming’s Sphere Packing Bound,– Gilbert … Web14 Jan 2024 · 3 Codes from designs held in a class of affine-invariant ternary codes. Let m\ge 5 be a positive integer, p be an odd prime and q = p^m. Let \gcd (m,l)=1 and … headphones good mic reddit

Two classes of new optimal ternary cyclic codes

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Web10 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. … Web10 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. goldsmiths worshipful companyWebIn 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. … headphones google. microphonenproblem

"Web1 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 … " - Ternary cyclic codes

Ternary cyclic codes

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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 … 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, …

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Web1 Jan 2016 · A class of optimal ternary cyclic codes and their duals. In this section, suppose that ( u, v) = ( ( 3 m + 1) / 2, 2 ⋅ 3 ℓ + 1) for an odd integer m = 2 ℓ + 1 ≥ 3. We shall study the …

WebCyclic Cipher chinese remainder theorem , data structures , implementation , number theory , two pointers 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 …

Web1 Jan 2024 · Li, N., Li, C., Helleseth, T., Ding, C., Tang, X.: Optimal ternary cyclic codes with minimum distance four and five. Finite Fields Appl. 30, 100–120 (2014) 28. Li, N., Zhou, Z., … 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. …

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 …

Web24 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 … headphones googleWebA 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 … headphones good qualityWebTwo 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 … headphones google pixel 6Webfamilies 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 … headphones google gamingWebCyclic codes as a subclass of linear codes have wide applications in communication systems, consumer electronics and data storage systems, due to their efficient encoding … goldsmiths worthingWebI 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 … goldsmiths wrexhamWeb5 Apr 2024 · Unpacking values from a regular expression match. When the regular expression exec() method finds a match, it returns an array containing first the entire … headphones google assistant disable