Advances in Coding Theory

The field of coding theory is witnessing significant developments, with a focus on constructing and analyzing new classes of codes with improved properties. Researchers are exploring extensions of existing code families, such as twisted Gabidulin codes and LCD codes, to achieve better performance and efficiency. Notably, there is a growing interest in designing codes with maximum rank distance and minimum distance separable properties, as well as investigating the covering radii and deep holes of these codes. Furthermore, advancements in computational complexity are being made, enabling the efficient computation of code distance and minimum size of trapping sets for certain classes of codes. Noteworthy papers include:

  • A study on twisted Gabidulin codes, which establishes necessary and sufficient conditions for them to be MRD codes and investigates their properties in the Hamming metric.
  • A paper on LDPC codes with bounded treewidth, which demonstrates a linear complexity algorithm for computing the minimum size of trapping sets.
  • A construction of four classes of LCD codes from (*)-(L,P)-twisted generalized Reed-Solomon codes, unifying previous results and providing new examples.
  • An improvement of constructions and lower bounds for maximally recoverable grid codes, providing new explicit constructions with polynomial field size and complementing them with field size lower bounds.

Sources

Three Classes of Twisted Gabidulin Codes with Different Twists

Linear Complexity Computation of Code Distance and Minimum Size of Trapping Sets for LDPC Codes with Bounded Treewidth

Four classes of LCD codes from (*)-(L,P)-twisted generalized Reed-Solomon codes

Improved Constructions and Lower Bounds for Maximally Recoverable Grid Codes

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