Advances in Coding Theory and Error-Correcting Codes

The field of coding theory is experiencing significant developments, with a focus on constructing and analyzing various types of error-correcting codes. Researchers are exploring new methods for constructing constant dimension codes, such as multilevel constructions, and investigating their applications in random network coding. Additionally, there is a growing interest in studying the weight enumerators of codes and their relationships to MacWilliams identities. Furthermore, researchers are working on improving lower bounds for conversion bandwidth in MDS convertible codes and constructing optimal ternary cyclic codes. Noteworthy papers in this area include: Several classes of three-weight or four-weight linear codes, which constructs projective three-weight and four-weight linear codes over F2 and determines their weight distributions. Improved AntiGriesmer Bounds for Linear Anticodes and Applications, which improves the antiGriesmer bound for linear anticodes and derives several corollaries, including lower bounds on the diameter and upper bounds on the code length. A Construction of Infinite Families of Self-Orthogonal Quasi-Cyclic Codes Using Constituent Codes, which proposes a construction of infinite families of quasi-cyclic codes that are self-orthogonal with respect to the Euclidean and Hermitian inner products.

Sources

Multilevel constructions of constant dimension codes based on one-factorization of complete graphs

Weight Enumerators From Equivalence Relations and MacWilliams Identities

An Elementary Approach to MacWilliams Extension Property and Constant Weight Code with Respect to Weighted Hamming Metric

Lower Bounds on Conversion Bandwidth for MDS Convertible Codes in Split Regime

On the Ding and Helleseth's 9th open problem about optimal ternary cyclic codes

Several classes of three-weight or four-weight linear codes

A Hypergraph based lower bound on Pliable Index Coding based on Nested Side-Information Sets

$\mathbb{F}_q\mathbb{F}_{q^2}$-additive cyclic codes and their Gray images

Improved AntiGriesmer Bounds for Linear Anticodes and Applications

A Construction of Infinite Families of Self-Orthogonal Quasi-Cyclic Codes Using Constituent Codes.pdf

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