相关论文: On a linear code from a configuration of affine li…

In this paper, we employ the linear systems representation of a convolutional code to develop a decoding algorithm for convolutional codes over the erasure channel. We study the decoding problem using the state space description and this…

In this work we explore error-correcting codes derived from the "lifting" of "affine-invariant" codes. Affine-invariant codes are simply linear codes whose coordinates are a vector space over a field and which are invariant under…

Based on the generic construction of linear codes, we construct linear codes over the ring $\Bbb Z_4$ via posets of the disjoint union of two chains. We determine the Lee weight distributions of the quaternary codes. Moreover, we obtain…

In this article, we consider the decoding problem of affine Grassmann codes over nonbinary fields. We use matrices of different ranks to construct a large set consisting of parity checks of affine Grassmann codes, which are orthogonal with…

We construct linear codes over the finite field Fq from arbitrary simplicial complexes, establishing a connection between topological properties and fundamental coding parameters. First, we study the behaviour of the weights of codewords…

We present a construction of subspace codes along with an efficient algorithm for list decoding from both insertions and deletions, handling an information-theoretically maximum fraction of these with polynomially small rate. Our…

We propose an algorithm for classification of linear codes over different finite fields based on canonical augmentation. We apply this algorithm to obtain classification results over fields with 2, 3 and 4 elements.

Assuming that we have a soft-decision list decoding algorithm of a linear code, a new hard-decision list decoding algorithm of its repeated code is proposed in this article. Although repeated codes are not used for encoding data, due to…

In this paper we give the generalization of lifted codes over any finite chain ring. This has been done by using the construction of finite chain rings from $p$-adic fields. Further we propose a lattice construction from linear codes over…

In this paper, we describe how to get Janet decomposition for a finite set of terms and detect completeness of that set by means of the associated Bar Code. Moreover, we explain an algorithm to find a variable ordering (if it exists) s.t. a…

Machine learning algorithms are typically run on large scale, distributed compute infrastructure that routinely face a number of unavailabilities such as failures and temporary slowdowns. Adding redundant computations using coding-theoretic…

The order statistics based list decoding techniques for linear binary block codes of small to medium block length are investigated. The construction of the list of the test error patterns is considered. The original order statistics…

In this paper, we consider minimal linear codes in a general construction of linear codes from q-ary functions. First, we give the sufficient and necessary condition for codewords to be minimal. Second, as an application, we present four…

In this paper we present an algorithm to compute the (real and complex) straight lines contained in a rational surface, defined by a rational parameterization. The algorithm relies on the well-known theorem of Differential Geometry that…

Linear codes with few weights have been an interesting subject of study for many years, as these codes have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, linear codes…

Interior-point algorithms constitute a very interesting class of algorithms for solving linear-programming problems. In this paper we study efficient implementations of such algorithms for solving the linear program that appears in the…

Here we study an efficient algorithm for decoding the topological codes. It is based on a simple principle, which should allow straightforward generalization to complex decoding problems. It is benchmarked with the planar code for both…

Recently, Chang and Hyun obtained some classes of binary optimal codes via simplicial complexes. In this letter, we utilize posets of the disjoint union of two chains to construct binary optimal linear codes.

We establish a connection between linear codes and hyperplane arrangements using the Thomas decomposition of polynomial systems and the resulting counting polynomial. This yields both a generalization and a refinement of the weight…

We analyze the list-decodability, and related notions, of random linear codes. This has been studied extensively before: there are many different parameter regimes and many different variants. Previous works have used complementary styles…