Advances in Coding Theory and Error Correction

The field of coding theory and error correction is moving towards the development of more efficient and robust methods for transmitting and storing data. Researchers are exploring new approaches to constructing optimal linear codes, such as those that achieve the Griesmer bound, and investigating the properties of these codes in various channels and scenarios. Additionally, there is a growing interest in the study of splitter sets and their applications in coding theory. The use of iterative methods and bounds, such as the linear programming bound, is becoming increasingly popular in the analysis of error-correcting codes. Furthermore, the development of new algorithms and techniques, such as fractional programming and tolerant testing, is enabling the construction of more efficient and effective codes. Noteworthy papers include: On the Error Exponent Distribution of Code Ensembles over Classical-Quantum Channels, which derives a threshold for the error exponent distribution of code ensembles over classical-quantum channels. On Construction of Approximate Real Mutually Unbiased Bases, which presents a method for constructing approximate real mutually unbiased bases for certain dimensions.

Sources

Lower Bounds for Error Coefficients of Griesmer Optimal Linear Codes via Iteration

On the Existence and Nonexistence of Splitter Sets

On the Convergence Speed of Spatially Coupled LDPC Ensembles Under Window Decoding

On the Error Exponent Distribution of Code Ensembles over Classical-Quantum Channels

Fractional Programming for Stochastic Precoding over Generalized Fading Channels

On Construction of Approximate Real Mutually Unbiased Bases for an infinite class of dimensions $d \not\equiv 0 \bmod 4$

Testing Isomorphism of Boolean Functions over Finite Abelian Groups

Linear codes for $b$-symbol read channels attaining the Griesmer bound

Generalized bilateral multilevel construction for constant dimension codes from parallel mixed dimension construction

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