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Open research questions in Coding theory and cryptography

98 gap statements mined from Coding theory and cryptography papers in our 4.5M-paper local library, which holds 516 papers on the topic — drawn mostly from each paper's own stated research gap, future-work, challenge and limitation notes, and its abstract. The ones listed below are a selection still marked open; each names the study that raised it, with a DOI link where the paper has one.

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What the literature leaves open

  • Future research may apply the results to cryptographic frameworks. Future research may apply the results to quantum graph-state models. Future research may extend the results to other types of graphs.

    An algebraic resolution of the ELSP via group actions in directed Paley graphs · 2026 · DOI

  • The ELSP problem was not previously resolved for directed Paley graphs. The problem of deciding local equivalence between graphs was not previously solved constructively.

    An algebraic resolution of the ELSP via group actions in directed Paley graphs · 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.

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

  • The need to prevent an eavesdropper from recovering parts of the message. The complexity of computing the exact leakage L(P).

    RankGuardPolar Private Public Finite Length Polar Codes with Rank-Certified Leakage · 2026

  • Future research can focus on extending the results of the paper to other types of codes. Future research can focus on applying the results of the paper to improve the design of error-correcting codes.

    On binary codes that are maximal totally isotropic subspaces with respect to an alternating form · 2026 · DOI

  • There is a gap in the understanding of the weight enumerator of the orthogonal complement of a binary linear code. The prior work on the MacWilliams identity for the weight enumerator of the dual of a binary linear code does not extend to the study of the weight enumerator of the orthogonal complement.

    On binary codes that are maximal totally isotropic subspaces with respect to an alternating form · 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

  • A gap in the classification of self-dual CR codes with covering radius ρ ≤ 3 is identified. The paper aims to close this gap.

    On maximum distance separable and completely regular 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 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 lack of an efficient method to find all pure gaps at many totally ramified places. The need for an explicit description of the set of pure gaps at many totally ramified places.

    Pure gaps at many places and multi-point AG codes from arbitrary Kummer extensions · 2026 · DOI

  • 4, 2025, it is still a 70-year-old open problem whether there is an infinite family of self-dual binary cyclic codes whose minimum distances have a lower bound better than the square-root bound.

    Four constructions of self-dual binary cyclic codes with a lower bound on the minimum distances better than the square-root bound · 2026

  • 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 paper does not provide a formal statement that justifies the need for adaptivity in Pollard's algorithm. The results are limited to the generic group model.

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

  • Future research can focus on constructing algebraic geometry codes with good properties using the results of the paper. The study of maximal function fields and their automorphism groups can be continued. The authors suggest exploring the applications of the results in coding theory and cryptography.

    The automorphism groups of a maximal function field with the second largest genus and its algebraic geometry codes · 2026 · DOI

  • The study addresses the need to construct long algebraic geometry codes with good properties.

    The automorphism groups of a maximal function field with the second largest genus and its algebraic geometry codes · 2026 · DOI

  • The paper shows that the ternary extended perfect Golay_3-code can be constructed using the modified GC-construction technique.

    On the ternary extended perfect Golay code by the modified GC-construction · 2026 · DOI

  • 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

  • To extend the RankGuard-Polar framework to other types of codes. To study the application of the RankGuard-Polar framework to different scenarios. To develop more efficient algorithms for computing the exact leakage L(P).

    RankGuardPolar Private Public Finite Length Polar Codes with Rank-Certified Leakage · 2026

  • 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

Most-cited papers in Coding theory and cryptography

Most recent work

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Open questions raised by papers listed on this page include: (1) Future research may apply the results to cryptographic frameworks (“An algebraic resolution of the ELSP via group actions in directed Paley graphs”, 2026); (2) 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); (3) The lack of a comprehensive understanding of linear codes with few weights (“Several classes of linear codes with at most six weights and their secret…”, 2026); (4) Future research can focus on extending the results of the paper to other types of codes (“On binary codes that are maximal totally isotropic subspaces with respect to an…”, 2026); (5) The lack of a precise bound on the length of near-MDS codes (“On the maximal length of near-MDS codes”, 2026). 98 gap statements have been mined from Coding theory and cryptography papers in our 4.5M-paper local library, which holds 516 papers on the topic; the gaps come from whichever of those papers state one. They are mostly the research gaps the authors state and the papers' abstracts, plus future-work, limitations and challenges passages. The ones listed below are a selection still marked open; each names the study that raised it, with a DOI link where the paper has one, so you can read the original claim in context.

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