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Open research questions in Coding theory and cryptography

78 unresolved questions extracted from the limitations and future-work sections of 253 Coding theory and cryptography papers in our library. Each links back to the study that raised it.

What the literature leaves open

  • The paper suggests investigating how to dimension the encryption scheme for a given security. The paper suggests exploring the use of Low Rank Parity-Check codes for cryptographic purposes.

    Gabidulin codes based post-quantum encryption schemes · 2026 · DOI

  • The paper identifies a gap in the design of post-quantum encryption schemes. The paper aims to fill this gap by presenting new promising directions in the design of encryption schemes.

    Gabidulin codes based post-quantum encryption schemes · 2026 · DOI

  • Further study of the properties of near-MDS codes. Investigation of the relationship between near-MDS codes and other types of codes. Exploration of potential applications of near-MDS codes.

    On the maximal length of near-MDS codes · 2026 · DOI

  • The lack of a precise bound on the length of near-MDS codes. The unclear relationship between near-MDS codes and almost-MDS codes.

    On the maximal length of near-MDS codes · 2026 · DOI

  • Future research can apply the verification technique to other codes. The technique can be used to study the weight distribution of other Reed-Muller codes.

    Verifying the computed weight distribution for the binary Reed–Muller Code R(4,9) · 2026 · DOI

  • The pseudorandomness of Hamming graphs makes them less susceptible to standard techniques. The study of VC-dimension requires analyzing the structure of the graph and the properties of subsets of its vertices. The paper needs to establish tight bounds on the size of a subset of vertices to guarantee VC-dimension 2 or 3.

    VC-dimension of subsets of Hamming graphs · 2026 · DOI

  • The paper focuses on the case where t = 1, and little is known about other values of t. The results are limited to the specific case of Hamming graphs and may not generalize to other types of graphs.

    VC-dimension of subsets of Hamming graphs · 2026 · DOI

  • The paper identifies the challenge of proving lower bounds on non-adaptive time-space tradeoffs. The results are limited to the generic group model. The paper seeks to understand classical generic algorithms for DLOG and other problems.

    Non-adaptive Cryptanalytic Time-Space Lower Bounds via a Shearer-Like Inequality for Permutations · 2026 · DOI

  • The complexity of the construction methods. The need to characterise the parameters of the resulting codes and designs in terms of the group invariants. The need to establish a duality for pairs of non-conjugate isomorphic maximal subgroups.

    Binary Linear Codes and Combinatorial Designs Constructed from the Alternating Groups A5, A7, and A9 · 2026 · DOI

  • The paper suggests future research on constructing more general self-orthogonal quasi-cyclic codes. The paper suggests future research on applying the constructed codes to practical quantum error correction scenarios.

    Construction of self-orthogonal quasi-cyclic codes and their application to quantum error-correcting codes · 2026 · DOI

  • The paper identifies a gap in prior work on the construction of self-orthogonal quasi-cyclic codes. The paper identifies a need for more general constructions of self-orthogonal quasi-cyclic codes.

    Construction of self-orthogonal quasi-cyclic codes and their application to quantum error-correcting codes · 2026 · DOI

  • Future research can focus on improving the lower bounds for other parameters of CDCs. Future research can explore other construction techniques for CDCs.

    Multilevel constructions of constant dimension codes based on one-factorization of complete graphs · 2026 · DOI

  • The paper identifies a gap in the existing literature on constructing CDCs. The paper identifies a need for improving the lower bounds of Aq(n, d, k).

    Multilevel constructions of constant dimension codes based on one-factorization of complete graphs · 2026 · DOI

  • The classification of self-orthogonal codes is incomplete. The existence of analogs of the dodecacode in other graphs is unknown.

    The punctured dodecacode is unique · 2026 · DOI

  • The need for a lower bound for q, - The complexity of choosing a proper parity-check matrix.

    Integer codes and their applications: an overview · 2026 · DOI

  • Constructing optimal p-ary cyclic codes is a challenging task. The paper needs to exploit algebraic properties of quartic characters.

    Several new classes of optimal p-ary cyclic codes · 2026 · DOI

  • Quantum errors due to decoherence and faulty gates, Limited resources for quantum error correction, Complexity of quantum error correction codes

    Entanglement-assisted Quasi-cyclic Quantum Low-density Parity-check Codes over Qubits · 2026 · DOI

  • The existence of genuinely unextendible product bases (GUPBs), incomplete orthogonal sets of fully product states whose orthogonal complements contain no product vector across any bipartition, has remained an open problem.

    Genuinely Unextendible Product Bases from Maximum Distance Separable Codes · 2026

  • We investigate the limit of lattices constructed from self-dual
Reed-Muller codes and provide evidence that they are sparse in this sense.

    Sparse modular forms, lattices, and codes · 2026 · DOI

  • We construct
families of modular forms that are sparse, such as the Eisenstein series E2k(τ ).

    Sparse modular forms, lattices, and codes · 2026 · DOI

  • The integer D q,k is not well understood. The Griesmer bound is not always attained.

    A conjecture on the minimum length of binary linear codes · 2026 · DOI

  • This formulation places classical cyclotomic cosets within a wider orbit theoretic setting and provides a new perspective for studying cyclotomic behavior through linear actions, contributing to the further study of orbit structures, invariants, and their advanced applications in finite fields, and group theory.

    On Cyclotomic Cosets as Orbit Structures under the Action of Cyclic Subgroups of GL(d,q) · 2026 · DOI

  • The gap is the need for a method to calculate linear codes associated with three-term exponential sums. The gap is the lack of analysis of the parameters, weight distributions, and distance properties of these codes.

    An MDS Code Generated from a Three-Term Exponential Sum · 2026 · DOI

  • The lack of a comprehensive understanding of linear codes with few weights. The need for constructing optimal or almost optimal linear codes with respect to the code table in [12].

    Several classes of linear codes with at most six weights and their secret sharing schemes · 2026 · DOI

  • Classifying MDS codes that are CR or uniformly packed in the wide sense is a challenging problem. Closing gaps in the classification of self-dual CR codes is a difficult task.

    On maximum distance separable and completely regular codes · 2026 · DOI

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78 open questions have been extracted from the limitations and future-work passages of 253 Coding theory and cryptography papers in our library. Each one below links back to the study that raised it, so you can read the original claim in context.

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