Related papers: Interleaving Loidreau's Rank-Metric Cryptosystem
Many algorithms are specified with respect to a fixed but unspecified parameter. Examples of this are especially common in cryptography, where protocols often feature a security parameter such as the bit length of a secret key. Our aim is…
We determine the probability, structure dependent, that the block Wiedemann algorithm correctly computes leading invariant factors. This leads to a tight lower bound for the probability, structure independent. We show, using block size…
We review the main results of the theory of rank-metric codes, with emphasis on their combinatorial properties. We study their duality theory and MacWilliams identities, comparing in particular rank-metric codes in vector and matrix…
We study error-correcting codes for permutations under the infinity norm, motivated by a novel storage scheme for flash memories call rank modulation. In this scheme, a set of $n$ flash cells are combined to create a single virtual…
Different variants of the code-based McEliece cryptosystem were pro- posed to reduce the size of the public key. All these variants use very structured codes, which open the door to new attacks exploiting the underlying structure. In this…
Clock synchronization has become a key design objective in wireless networks for its essential importance in many applications. However, as the wireless link is prone to random network delays due to unreliable channel conditions, it is in…
Probability estimation is an elementary building block of every statistical data compression algorithm. In practice probability estimation is often based on relative letter frequencies which get scaled down, when their sum is too large.…
Several applications in communication, control, and learning require approximating target distributions to within small informational divergence (I-divergence). The additional requirement of invertibility usually leads to using encoders…
In this paper, we focus on developing randomized algorithms for the computation of low multilinear rank approximations of tensors based on the random projection and the singular value decomposition. Following the theory of the singular…
In this paper the ensemble of codes formed by a serial concatenation of a repetition code with multiple accumulators connected through random interleavers is considered. Based on finite length weight enumerators for these codes, asymptotic…
Low-rank parity-check (LRPC) codes are the rank-metric analogue of low-density parity-check codes and they found important applications in code-based cryptography. In this paper we investigate a sub-family of LRPC codes, which have a…
To facilitate applications in IoT, 5G, and beyond, there is an engineering need to enable high-rate, low-latency communications. Errors in physical channels typically arrive in clumps, but most decoders are designed assuming that channels…
The McEliece scheme is a generic frame which allows to use any error correcting code of which there exists an efficient decoding algorithm to design an encryption scheme by hiding the generator matrix code. Similarly, the Niederreiter frame…
Latent variable models are well-known to suffer from rank deficiencies, causing problems with convergence and stability. Such problems are compounded in the "reduced-group split-ballot multitrait-multimethod model", which omits a set of…
Low-density parity-check (LDPC) codes are one of the most promising families of codes to replace the Goppa codes originally used in the McEliece cryptosystem. In fact, it has been shown that by using quasi-cyclic low-density parity-check…
We study the performance of nonbinary low-density parity-check (LDPC) codes over finite integer rings over two channels that arise from the Lee metric. The first channel is a discrete memory-less channel (DMC) matched to the Lee metric. The…
Lifted Reed-Solomon and multiplicity codes are classes of codes, constructed from specific sets of $m$-variate polynomials. These codes allow for the design of high-rate codes that can recover every codeword or information symbol from many…
Minimal rank-metric codes or, equivalently, linear cutting blocking sets are characterized in terms of the second generalized rank weight, via their connection with evasiveness properties of the associated $q$-system. Using this result, we…
The routing algorithms for parallel computers, on-chip networks, multi-core processors, and multiprocessors system-on-chip (MP-SoCs) exhibit router failures must be able to handle interconnect router failures that render a symmetrical mesh…
We give a recursive construction for projective Reed-Muller codes in terms of affine Reed-Muller codes and projective Reed-Muller codes in fewer variables. From this construction, we obtain the dimension of the subfield subcodes of…