Related papers: Minimal Linear Codes Constructed from Functions
Linear codes with few weights have applications in consumer electronics, communication, data storage system, secret sharing, authentication codes, association schemes, and strongly regular graphs. This paper first generalizes the method of…
Linear codes have been an interesting subject of study for many years, as linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, a class of…
This paper examines linear binary codes capable of correcting one or more errors. For the single-error-correcting case, it is shown that the Hamming bound is achieved by a constructive method, and an exact expression for the minimal…
This work investigates the structure of rank-metric codes in connection with concepts from finite geometry, most notably the $q$-analogues of projective systems and blocking sets. We also illustrate how to associate a classical…
Based on ideas of K\"otter and Kschischang we use constant dimension subspaces as codewords in a network. We show a connection to the theory of q-analogues of a combinatorial designs, which has been studied in Braun, Kerber and Laue as a…
We present new constructions of binary quantum codes from quaternary linear Hermitian self-dual codes. Our main ingredients for these constructions are nearly self-orthogonal cyclic or duadic codes over F_4. An infinite family of…
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, monomials and trinomials over…
It is reasonable to expect the theory of quantum codes to be simplified in the case of codes of minimum distance 2; thus, it makes sense to examine such codes in the hopes that techniques that prove effective there will generalize. With…
Codes considered as structures within unit schemes greatly extends the availability of linear block and convolutional codes and allows the construction of these codes to required length, rate, distance and type. Properties of a code emanate…
In this paper, we first study in detail the relationship between minimal linear codes and cutting blocking sets, which were recently introduced by Bonini and Borello, and then completely characterize minimal linear codes as cutting blocking…
Linear complementary-dual (LCD for short) codes are linear codes that intersect with their duals trivially. LCD codes have been used in certain communication systems. It is recently found that LCD codes can be applied in cryptography. This…
Binary matrix codes with restricted row and column weights are a desirable method of coded modulation for power line communication. In this work, we construct such matrix codes that are obtained as products of affine codes - cosets of…
Subspace codes are the $q$-analog of binary block codes in the Hamming metric. Here the codewords are vector spaces over a finite field. They have e.g. applications in random linear network coding, distributed storage, and cryptography. In…
Locally recoverable codes (LRCs) were proposed for the recovery of data in distributed and cloud storage systems about nine years ago. A lot of progress on the study of LRCs has been made by now. However, there is a lack of general theory…
Boolean functions with high algebraic immunity are important cryptographic primitives in some stream ciphers. In this paper, two methodologies for constructing binary minimal codes from sets, Boolean functions and vectorial Boolean…
In this paper we generalize constructions in two recent works of Ding, Heng, Zhou to any field $\mathbb{F}_q$, $q$ odd, providing infinite families of minimal codes for which the Ashikhmin-Barg bound does not hold.
Recently, many good quantum codes over various finite fields $F_q$ have been constructed from codes over extension rings or mixed alphabet rings via some version of a Gray map. We show that most of these codes can be obtained more directly…
In this paper, we develop the python code for generating unit graph $G(\mathbb{Z}_{n}\oplus\mathbb{Z}_{m})$, for any integers $m\ \& \ n$. For any prime $r$, we construct $r$-ary linear codes from the incidence matrix of the unit graph…
Recently, simplicial complexes are used in constructions of several infinite families of minimal and optimal linear codes by Hyun {\em et al.} Building upon their research, in this paper more linear codes over the ring $\mathbb{Z}_4$ are…
Certain simplicial complexes are used to construct a subset $D$ of $\mathbb{F}_{2^n}^m$ and $D$, in turn, defines the linear code $C_{D}$ over $\mathbb{F}_{2^n}$ that consists of $(v\cdot d)_{d\in D}$ for $v\in \mathbb{F}_{2^n}^m$. Here we…