Advances in Error-Correction and Coding Theory

The field of error-correction and coding theory is witnessing significant developments, with a focus on improving the efficiency and reliability of coding schemes. Recent research has explored new constructions and bounds for various types of codes, including polar codes, LDPC codes, and flag codes. Notably, there is a growing interest in designing codes with enhanced weight distribution, which is crucial for achieving optimal error-correction performance. Additionally, researchers are investigating the application of coding theory to emerging areas, such as molecular communication and covert communication. Noteworthy papers in this area include the proposal of a new structure for polar codes to improve polarization on channels with memory, and the development of novel constructions for full flag codes based on partial spreads. The paper on the complete weight distribution of a family of irreducible cyclic codes of dimension two also presents significant findings, enabling the construction of optimal systematic authentication codes.

Sources

Bounds and New Constructions for Girth-Constrained Regular Bipartite Graphs

On the High-Rate FDPC Codes: Construction, Encoding, and a Generalization

The complete weight distribution of a family of irreducible cyclic codes of dimension two

On Differential and Boomerang Properties of a Class of Binomials over Finite Fields of Odd Characteristic

Last-Pair Swapping Polar Codes: A Structure to Improve Polarization on Channels with Memory

Identification for Molecular Communication Based on Diffusion Channel with Poisson Reception Process

Covert Capacity of AWGN Channels under Average Error Probability

The Ultimate Signs of Second-Order Holonomic Sequences

Joint Error Correction and Fading Channel Estimation Enhancement Leveraging GRAND

New Constructions of Full Flag Codes Based on Partial Spreads

New Bounds and Constructions for Variable Packet-Error Coding

Towards Weight Distribution-Aware Polar Codes

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