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Maximum Distance Profile (MDP) convolutional codes are an important class of channel codes due to their maximal delay-constrained error correction capabilities. The design of MDP codes has attracted significant attention from the research…
Generalized Reed-Solomon codes form the most prominent class of maximum distance separable (MDS) codes, codes that are optimal in the sense that their minimum distance cannot be improved for a given length and code size. The study of codes…
Dihedral codes, particular cases of quasi-cyclic codes, have a nice algebraic structure which allows to store them efficiently. In this paper, we investigate it and prove some lower bounds on their dimension and minimum distance, in analogy…
We prove that a class of distance-optimal local reconstruction codes (LRCs), an important family of repair-efficient codes for distributed storage systems, achieve the maximum distance separable private information retrieval capacity for…
We study permutations over the set of $\ell$-grams, that are feasible in the sense that there is a sequence whose $\ell$-gram frequency has the same ranking as the permutation. Codes, which are sets of feasible permutations, protect…
In this paper we present several classes of asymptotically good concatenated quantum codes and derive lower bounds on the minimum distance and rate of the codes. We compare these bounds with the best-known bound of…
Binary cyclic codes having large dimensions and minimum distances close to the square-root bound are highly valuable in applications where high-rate transmission and robust error correction are both essential. They provide an optimal…
In order to overcome the challenges caused by flash memories and also to protect against errors related to reading information stored in DNA molecules in the shotgun sequencing method, the rank modulation is proposed. In the rank modulation…
Fractional repetition (FR) codes are a class of repair efficient erasure codes that can recover a failed storage node with both optimal repair bandwidth and complexity. In this paper, we study the minimum distance of FR codes, which is the…
A family of distance-optimal LRC codes from certain subcodes of $q$-ary Reed-Solomon codes, proposed by I.~Tamo and A.~Barg in 2014, assumes that the code length $n$ is a multiple of $r+1.$ By shortening codes from this family, we show that…
The decomposition of a quasi-abelian code into shorter linear codes over larger alphabets was given in (Jitman, Ling, (2015)), extending the analogous Chinese remainder decomposition of quasi-cyclic codes (Ling, Sol\'e, (2001)). We give a…
In this paper we introduce a new type of code, called projective nested cartesian code. It is obtained by the evaluation of homogeneous polynomials of a fixed degree on a certain subset of $\mathbb{P}^n(\mathbb{F}_q)$, and they may be seen…
The main result here is a characterisation of binary $2$-neighbour-transitive codes with minimum distance at least $5$ via their minimal subcodes, which are found to be generated by certain designs. The motivation for studying this class of…
Exponential divided differences arise in numerical linear algebra, matrix-function evaluation, and quantum Monte Carlo simulations, where they serve as kernel weights for time evolution and observable estimation. Efficient and numerically…
In this paper we study spread codes: a family of constant-dimension codes for random linear network coding. In other words, the codewords are full-rank matrices of size (k x n) with entries in a finite field F_q. Spread codes are a family…
We survey permutation-based methods for approximate k-nearest neighbor search. In these methods, every data point is represented by a ranked list of pivots sorted by the distance to this point. Such ranked lists are called permutations. The…
A classical recursive construction for mutually orthogonal latin squares (MOLS) is shown to hold more generally for a class of permutation codes of length $n$ and minimum distance $n-1$. When such codes of length $p+1$ are included as…
By extending the notion of minimum rank distance, this paper introduces two new relative code parameters of a linear code C_1 of length n over a field extension and its subcode C_2. One is called the relative dimension/intersection profile…
We develop a new family of linear programs, that yield upper bounds on the rate of binary linear codes of a given distance. Our bounds apply {\em only to linear codes.} Delsarte's LP is the weakest member of this family and our LP yields…
The minimum distance of expander codes over GF(q) is studied. A new upper bound on the minimum distance of expander codes is derived. The bound is shown to lie under the Varshamov-Gilbert (VG) bound while q >= 32. Lower bounds on the…