Related papers: Constructions of Batch Codes via Finite Geometry
We introduce a random coding technique for transmission over discrete memoryless channels, reminiscent of the basic construction attaining the Gilbert-Varshamov bound for codes in Hamming spaces. The code construction is based on drawing…
It is well-known that cyclic codes have efficient encoding and decoding algorithms. In recent years, antiprimitive BCH codes have attracted a lot of attention. The objective of this paper is to study BCH codes of this type over finite…
A weakly constrained code is a collection of finite-length strings over a finite alphabet in which certain substrings or patterns occur according to some prescribed frequencies. Buzaglo and Siegel (ITW 2017) gave a construction of weakly…
The paper presents a method to generate some families of linear codes over finite fields of characteristics greater than two in the widest class due to the size of Grassmann manifold, i.e. when the dimension is equal to codimension. Our…
We generalize the notion of cyclic codes by using generator polynomials in (non commutative) skew polynomial rings. Since skew polynomial rings are left and right euclidean, the obtained codes share most properties of cyclic codes. Since…
Algebraic-geometric codes can be constructed by evaluating a certain set of functions on a set of distinct rational points of an algebraic curve. The set of functions that are evaluated is the linear space of a given divisor or,…
One central theme in quantum error-correction is to construct quantum codes that have a large minimum distance. In this paper, we first present a construction of classical codes based on certain class of polynomials. Through these classical…
Basic algebraic and combinatorial properties of finite vector spaces in which individual vectors are allowed to have multiplicities larger than $ 1 $ are derived. An application in coding theory is illustrated by showing that multispace…
In this note, we present a construction of new nonbinary quantum codes with good parameters. These codes are obtained by applying the Calderbank-Shor-Steane (CSS) construction. In order to do this, we show the existence of (classical)…
Batch codes, first introduced by Ishai, Kushilevitz, Ostrovsky, and Sahai, mimic a distributed storage of a set of $n$ data items on $m$ servers, in such a way that any batch of $k$ data items can be retrieved by reading at most some $t$…
A pattern of a sequence is a sequence of integer indices with each index describing the order of first occurrence of the respective symbol in the original sequence. In a recent paper, tight general bounds on the block entropy of patterns of…
A new class of spherical codes is constructed by selecting a finite subset of flat tori from a foliation of the unit sphere S^{2L-1} of R^{2L} and designing a structured codebook on each torus layer. The resulting spherical code can be the…
Constrained coding plays a key role in optimizing performance and mitigating errors in applications such as storage and communication, where specific constraints on codewords are required. While non-parametric constraints have been…
The notion of a two-dimensional word arises naturally in the study of combinatorics on words, while the iterative construction of pedal triangles results in a rich dynamical system in the study of geometry. At first, these two classes of…
Affine-invariant codes have attracted considerable attention due to their rich algebraic structure and strong theoretical properties. In this paper, we study a family of affine-invariant codes whose defining set consists of all descendants…
Constant dimension codes are subsets of the finite Grassmann variety. The study of these codes is a central topic in random linear network coding theory. Orbit codes represent a subclass of constant dimension codes. They are defined as…
The classical way of extending an $[n, k, d]$ linear code $\C$ is to add an overall parity-check coordinate to each codeword of the linear code $\C$. This extended code, denoted by $\overline{\C}(-\bone)$ and called the standardly extended…
In many sequence learning tasks, such as program synthesis and document summarization, a key problem is searching over a large space of possible output sequences. We propose to learn representations of the outputs that are specifically…
This paper proposes a polar code construction scheme that reduces constituent-code supplemented decoding latency. Constituent codes are the sub-codewords with specific patterns. They are used to accelerate the successive cancellation…
An iterative decoding algorithm for convolutional codes is presented. It successively processes $N$ consecutive blocks of the received word in order to decode the first block. A bound is presented showing which error configurations can be…