2024 Ternary cyclic codes

Ternary cyclic codes

Author: cklf

August undefined, 2024

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 …

Further results on optimal ternary cyclic codes Request PDF

Web5 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 … WebA: 1. Since each page has a size of 256 bytes, the offset will require 8 bits to represent all possible…. Q: I'd be grateful for any kind of explanation of what an optimising compiler is … cooking with fruit juice

On the minimum distance of ternary cyclic codes - Information …

Web13 Mar 2024 · Four infinite families of ternary cyclic codes with a square-root-like lower bound ... Cyclic codes are an interesting type of linear codes and have wide applications … 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. … 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, … cooking with frozen fruit

"Five Families of Three-Weight Ternary Cyclic Codes and Their

Web6 Mar 2024 · t. e. In coding theory, the ternary Golay codes are two closely related error-correcting codes. The code generally known simply as the ternary Golay code is an [ 11, 6, … 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 … cooking with frozen vegetablesWeb31 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 … cooking with frozen spinach

"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 … " - Ternary cyclic codes

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 … 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 …

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WebThe codes that we use here are the well known Golay codes. These codes are among the most beautiful objects in coding theory, and we would like to give some reasons why. … Web1 Oct 2024 · The ternary cyclic code C (1, e) has parameters [3 m − 1, 3 m − 1 − 2 m, 4] if and only if the following conditions are satisfied: (1) e is even; (2) (x + 1) e + x e + 1 = 0 has the …

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 … WebNow, we will begin the discussion of cyclic codes explicitly with error detection and correction. Cyclic codes can be used to correct errors, like Hamming codes as cyclic …

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. 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 …

Web6 Apr 2024 · Catalytic cyclic distillation (CCD) exploits the synergies of combined reaction and separation by manipulating the duration of an event (e.g., residence time) in a cyclic …

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., … cooking with gabyWebgroup 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 … cooking with garlic chives recipesWeb5 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 … cooking with garlic juiceWebIMP: 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 … family guy peter and bonnieWeb1 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 … cooking with garlic scapesWebfamilies 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 … cooking with frozen zucchiniWeb24 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 … cooking with gas christchurch