Additive cyclic codes over mixed alphabets and the football pool problem

2017 ◽  
Vol 09 (01) ◽  
pp. 1750010
Author(s):  
Taher Abualrub ◽  
N. Aydin
Keyword(s):  
Cyclic Codes ◽  
Optimal Parameters ◽  
Generating Sets ◽  
Algebraic Properties

Motivated by a generalization of the football pool problem, we introduce additive cyclic codes over mixed alphabets of the form [Formula: see text] where [Formula: see text], [Formula: see text] for distinct primes [Formula: see text]. We study their algebraic properties, generating sets, and duals. Additionally, we give examples of additive cyclic codes over the alphabet [Formula: see text] that have best-known or optimal parameters.

A Family of q-Ary Cyclic Codes with Optimal Parameters

2020 ◽  
Vol E103.A (3) ◽  
pp. 631-633
Author(s):  
Wenhua ZHANG ◽  
Shidong ZHANG ◽  
Yong WANG ◽  
Jianpeng WANG
Keyword(s):  
Cyclic Codes ◽  
Optimal Parameters

Triple Cyclic Codes Over 𝔽q + u𝔽q

2021 ◽  
pp. 1-21
Author(s):  
Ting Yao ◽  
Shixin Zhu ◽  
Binbin Pang
Keyword(s):  
Special Class ◽  
Linear Codes ◽  
Cyclic Code ◽  
Cyclic Codes ◽  
Cyclic Shift ◽  
Generating Sets ◽  
Optimal Linear ◽  
Number Formula ◽  
The Relationship ◽  
Optimal Linear Codes

Let [Formula: see text], where [Formula: see text] is a power of a prime number [Formula: see text] and [Formula: see text]. A triple cyclic code of length [Formula: see text] over [Formula: see text] 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 codes can be viewed as [Formula: see text]-submodules of [Formula: see text]. In this paper, we study the generator polynomials and the minimum generating sets of this kind of codes. Some optimal or almost optimal linear codes are obtained from this family of codes. We present the relationship between the generators of triple cyclic codes and their duals. As a special class of triple cyclic codes, separable codes over [Formula: see text] are discussed briefly in the end.

Optimal parameters for hydraulic generating sets at small HPP

2010 ◽  
Vol 44 (2) ◽  
pp. 87-90
Author(s):  
A. V. Tarasov ◽  
G. I. Topazh
Keyword(s):  
Optimal Parameters ◽  
Generating Sets

Some results on cyclic codes over ℤq + uℤq

2015 ◽  
Vol 07 (04) ◽  
pp. 1550058 ◽  
Author(s):  
Jian Gao ◽  
Fang-Wei Fu ◽  
Ling Xiao ◽  
Rama Krishna Bandi
Keyword(s):  
Hamming Distance ◽  
Cyclic Codes ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Generating Sets ◽  
Minimum Hamming Distance ◽  
Necessary And Sufficient

Let [Formula: see text], where [Formula: see text] and [Formula: see text]. In this paper, minimum generating sets of cyclic codes over [Formula: see text] are given. A necessary and sufficient condition for cyclic codes over [Formula: see text] to be [Formula: see text]-free is obtained and a BCH-type bound on the minimum Hamming distance for them is also given.

Quasi-cyclic codes: algebraic properties and applications

2020 ◽  
Vol 39 (2) ◽  
Author(s):  
Mohamadbagher Zeraatpisheh ◽  
Morteza Esmaeili ◽  
T. Aaron Gulliver
Keyword(s):  
Cyclic Codes ◽  
Algebraic Properties ◽  
Quasi Cyclic Codes

scholarly journals Double Cyclic Codes over \({\mathbb{F}_{q}+v\mathbb{F}_{q}}\)

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1820
Author(s):  
Tenghui Deng ◽  
Jing Yang
Keyword(s):  
Algebraic Structure ◽  
Cyclic Codes ◽  
Dual Codes ◽  
Generating Sets ◽  
Special Cases

In this paper, an algebraic structure of a type of double cyclic codes is investigated, which covers some existing codes as special cases. The paper presents generic results about the generating polynomials, minimal generating sets, matrices and dual codes of the proposed codes.

Main problems of import subsumption in domestic engineering, applicable to small-power electric generator installations

2018 ◽  
Vol 1 (1) ◽  
pp. 46-51 ◽  
Author(s):  
A. V. Shelgunov
Keyword(s):  
Low Power ◽  
Import Substitution ◽  
Power Generator ◽  
Small Power ◽  
Domestic Production ◽  
Power Generators ◽  
Electric Generator ◽  
Generating Sets ◽  
Current State ◽  
Generator Sets

Subject: the subject of the study are low-power generator sets with a power of up to 30 kW.Materials and methods: in this paper, the main domestic legislative documents regulating the requirements for products. An assessment is made of the current state of Russian engine building.Results: the detailed analysis of the modern domestic market of power generating units with a capacity of up to 30 kW is made, the main problems in the field of domestic production of  electric power generators in the range up to 30 kW are revealed, and the prospects for import substitution of gasoline and diesel engines are noted.Conclusions: almost complete absence of the market of domestic low-power generating sets is established, insufficient measures taken to support domestic producers are noted, measures are  proposed for the development of domestic production of power units in the range of up to 30 kW.

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