Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Minimal Linear Codes Constructed from Sunflowers
View through CrossRef
Sunflower in coding theory is a class of important subspace codes and can be used to construct linear codes. In this paper, we study the minimality of linear codes over Fq constructed from sunflowers of size s in all cases. For any sunflower, the corresponding linear code is minimal if s≥q+1, and not minimal if 2≤s≤3≤q. In the case where 3<s≤q, for some sunflowers, the corresponding linear codes are minimal, whereas for some other sunflowers, the corresponding linear codes are not minimal.
Title: Minimal Linear Codes Constructed from Sunflowers
Description:
Sunflower in coding theory is a class of important subspace codes and can be used to construct linear codes.
In this paper, we study the minimality of linear codes over Fq constructed from sunflowers of size s in all cases.
For any sunflower, the corresponding linear code is minimal if s≥q+1, and not minimal if 2≤s≤3≤q.
In the case where 3<s≤q, for some sunflowers, the corresponding linear codes are minimal, whereas for some other sunflowers, the corresponding linear codes are not minimal.
Related Results
Sunflowers
Sunflowers
Whatever a work of art may be, the artist certainly cannot dare to be simple. (Rebecca West)
Van Gogh's Sunflowers is [not] conside...
Generalised array low‐density parity‐check codes
Generalised array low‐density parity‐check codes
In this study, using Group Permutation Low‐Density Parity‐Check (GP‐LDPC) codes, the authors generalise the concept of array Low‐Density Parity‐Check (LDPC) codes from fields of pr...
Two-Module Weight-Based Sum Code in Residue Ring Modulo M=4
Two-Module Weight-Based Sum Code in Residue Ring Modulo M=4
The paper describes research results of features of error detection in data vectors by sum codes. The task is relevant in this setting, first of all, for the use of sum codes in th...
Self-dual codes over $\mathbb{F}_{q}+u\mathbb{F}_{q}+u^2\mathbb{F}_{q}$ and applications
Self-dual codes over $\mathbb{F}_{q}+u\mathbb{F}_{q}+u^2\mathbb{F}_{q}$ and applications
Self-dual codes over finite fields and over some finite rings have been of interest and extensively studied due to their nice algebraic structures and wide applications. Recently, ...
Properties of Fuzzy Soft Codes and Their Role in Decision-Making
Properties of Fuzzy Soft Codes and Their Role in Decision-Making
Background Fuzzy soft sets are well-established for decision-making under uncertainty. However, integrating soft set theory with fuzzy codes remains unexplored, as fuzzy soft code ...
Quasi~λ-cyclic Codes Over a Class of Finite Commutative Semi-simple Rings
Quasi~λ-cyclic Codes Over a Class of Finite Commutative Semi-simple Rings
Abstract
In coding theory, quasi λ-cyclic codes form an important class of codes which have been extensively studied. In this paper, we investigate the algebraic structure ...
Treatment Performance Assessment of Natural and Constructed Wetlands on Wastewater From Kege Wet Coffee Processing Plant in Dale Woreda, Sidama Regional State, Ethiopia
Treatment Performance Assessment of Natural and Constructed Wetlands on Wastewater From Kege Wet Coffee Processing Plant in Dale Woreda, Sidama Regional State, Ethiopia
Constructed wetlands are engineered systems built to use natural processes and remove pollutants from contaminated water in a more controlled environment. The research was an exper...
188-OR: Assessing the Validity of Diagnosis Codes for Gestational Diabetes Ascertainment
188-OR: Assessing the Validity of Diagnosis Codes for Gestational Diabetes Ascertainment
Background: Researchers often rely on diagnosis codes from billing/administrative data to ascertain diagnoses, including gestational diabetes (GDM). We assessed the validity of rel...