arXiv subjects

Ousmane Ndiaye

Publications and source records attributed to Ousmane Ndiaye.

4 recordsLinked to original sources

arXiv2026

Twisted Conjugacy and the Classification of Induced Centrosymmetric Alternant Codes

This paper presents a classification of induced centrosymmetric alternant codes through the study of the automorphism structures inherited from Generalized Reed--Solomon (GRS) codes. We introduce the twisted conjugation action naturally associated with projective semilinear transformations and establish its correspondence with ordinary conjugacy in the projective semilinear group. This correspondence enables the application of Shintani's theorem to classify the $γ_{p^j}$-similarity classes of involutions. As a consequence, we obtain necessary and sufficient conditions for an alternant code to admit a centrosymmetric structure induced by a projective semilinear automorphism. The resulting classification unifies the different families of induced centrosymmetric alternant codes within a common automorphism-based framework.

cs.IT↗

arXiv2026

Subcodes of Lambda-Gabidulin Codes for Compact-Ciphertext Cryptography

This paper investigates subcodes of lambda-Gabidulin codes, viewed as rank-metric analogues of generalized Reed--Solomon codes, and their applications to compact-ciphertext cryptosystems. We first analyze subspace and generalized subspace subcodes of lambda-Gabidulin codes and relate them to corresponding subcodes of classical Gabidulin codes through coordinate-wise scaling. This relation yields cardinality bounds and structural properties for these families. When the extension degree equals the code length, we further characterize Gabidulin subspace subcodes in terms of linearized polynomials, which gives an explicit description of their encoding and dimension. We also study the matrix images of these subcodes over the base field through their stabilizer and annihilator algebras, showing that subspace restrictions may preserve nontrivial algebraic invariants despite the loss of extension-field linearity. Motivated by these results, we propose a generator-matrix-based construction of random subcodes designed to avoid such invariants. This construction is then used to design McEliece-like and Niederreiter-like encryption schemes in the MinRank setting. Among the parameter sets considered in this work, the most compact ciphertexts are obtained from random subcodes of classical Gabidulin codes. At the 128-, 192-, and 256-bit security levels, the resulting $\mathsf{LGS}$-Niederreiter instances achieve the smallest ciphertext sizes among the compared schemes, while maintaining competitive public-key sizes.

cs.CR↗

arXiv2023

Generalized Subspace Subcodes in the Rank Metric

Rank-metric codes were studied by E. Gabidulin in 1985 after a brief introduction by Delsarte in 1978 as an equivalent of Reed-Solomon codes, but based on linearized polynomials. They have found applications in many areas, including linear network coding and space-time coding. They are also used in cryptography to reduce the size of the keys compared to Hamming metric codes at the same level of security. However, some families of rank-metric codes suffer from structural attacks due to the strong algebraic structure from which they are defined. It therefore becomes interesting to find new code families in order to address these questions in the landscape of rank-metric codes. \par In this paper, we provide a generalization of Subspace Subcodes in Rank metric introduced by Gabidulin and Loidreau. We also characterize this family by giving an algorithm which allows to have its generator and parity-check matrices based on the associated extended codes. We have also studied the specific case of Gabidulin codes whose underlying decoding algorithms are known. Bounds for the cardinalities of these codes, both in the general case and in the case of Gabidulin codes, are also provided.

cs.IT↗

arXiv2015

One Cyclic Codes over $\mathbb{F}_{p^k} + v\mathbb{F}_{p^k} + v^2\mathbb{F}_{p^k} + ... + v^r\mathbb{F}_{p^k}$

In this paper, we investigate cyclic code over the ring $\mathbb{F}_{p^k} + v\mathbb{F}_{p^k} + v^2\mathbb{F}_{p^k} + ... + v^r\mathbb{F}_{p^k}$, where $v^{r+1}=v$, $p$ a prime number, $r>1$ and $\gcd(r,p)=1$, we prove as generalisation of P. Solé et al. in 2015 that these codes are principally generated, give generator polynomial and idempotent depending on idempotents over this ring as response to an open problem related by J. QIAN et al. in 2005. we also give a gray map and proprieties of the related dual code.

cs.IT↗