Problems on q-Analogs in Coding Theory

Abstract

The interest in $q$-analogs of codes and designs has been increased in the last few years as a consequence of their new application in error-correction for random network coding. There are many interesting theoretical, algebraic, and combinatorial coding problems concerning these q-analogs which remained unsolved. The first goal of this paper is to make a short summary of the large amount of research which was done in the area mainly in the last few years and to provide most of the relevant references. The second goal of this paper is to present one hundred open questions and problems for future research, whose solution will advance the knowledge in this area. The third goal of this paper is to present and start some directions in solving some of these problems.

arXiv admin note: text overlap with arXiv:0805.3528 by other authors

References in corpus (7)

• Automorphisms of Codes in the Grassmann Scheme
• List Decoding of Lifted Gabidulin Codes via the Plücker Embedding
• List decoding subspace codes from insertions and deletions
• Decoding of Subspace Codes, a Problem of Schubert Calculus over Finite Fields
• The q-Analog of the Middle Levels Problem
• Large Sets of $t$-Designs over Finite Fields
• Partial k-Parallelisms in Finite Projective Spaces

Cited by in corpus (6)

• Tables of subspace codes
• Optimal Binary Subspace Codes of Length 6, Constant Dimension 3 and Minimum Distance 4
• The Expurgation-Augmentation Method for Constructing Good Plane Subspace Codes
• Construction of Const Dimension Code from Two Parallel Versions of Linkage Construction
• Intersection Patterns in Optimal Binary $(5,3)$ Doubling Subspace Codes
• Necessary conditions for the existence of 3-designs over finite fields with nontrivial automorphism groups