Related papers: On q-ary codes with two distances d and d+1
Constant-dimension codes have recently received attention due to their significance to error control in noncoherent random linear network coding. What the maximal cardinality of any constant-dimension code with finite dimension and minimum…
A $q$-ary $(n,k,r)$ locally repairable code (LRC) is an $[n,k,d]$ linear code over $\mathbb{F}_q$ such that every code symbol can be recovered by accessing at most $r$ other code symbols. The well-known Singleton-like bound says that $d \le…
For nonnegative integers $n_2, n_3$ and $d$, let $N(n_2,n_3,d)$ denote the maximum cardinality of a code of length $n_2+n_3$, with $n_2$ binary coordinates and $n_3$ ternary coordinates (in this order) and with minimum distance at least…
In this paper we study flag codes of maximum distance. We characterize these codes in terms of, at most, two relevant constant dimension codes naturally associated to them. We do this first for general flag codes and then particularize to…
In the context of constant--dimension subspace codes, an important problem is to determine the largest possible size $A_q(n, d; k)$ of codes whose codewords are $k$-subspaces of $\mathbb{F}_q^n$ with minimum subspace distance $d$. Here in…
Additive codes may have better parameters than linear codes. However, still very few cases are known and the explicit construction of such codes is a challenging problem. Here we show that a Griesmer type bound for the length of additive…
Lifted maximum rank distance (MRD) codes, which are constant dimension codes, are considered. It is shown that a lifted MRD code can be represented in such a way that it forms a block design known as a transversal design. A slightly…
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…
Binary cyclic codes are worth studying due to their applications and theoretical importance. It is an important problem to construct an infinite family of cyclic codes with large minimum distance $d$ and dual distance $d^{\perp}$. In recent…
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…
A linear code with parameters $[n, k, n - k + 1]$ is called maximum distance separable (MDS), and one with parameters $[n, k, n - k]$ is called almost MDS (AMDS). A code is near-MDS (NMDS) if both it and its dual are AMDS. NMDS codes…
In [1] a syndrome counting based upper bound on the minimum distance of regular binary LDPC codes is given. In this paper we extend the bound to the case of irregular and generalized LDPC codes over GF(q). The comparison to the lower bound…
A new approach to bound the minimum distance of $q$-ary cyclic codes is presented. The connection to the BCH and the Hartmann--Tzeng bound is formulated and it is shown that for several cases an improvement is achieved. We associate a…
Minimal codes are linear codes where all non-zero codewords are minimal, i.e., whose support is not properly contained in the support of another codeword. The minimum possible length of such a $k$-dimensional linear code over $\mathbb{F}_q$…
Recently, subfield codes of geometric codes over large finite fields $\gf(q)$ with dimension $3$ and $4$ were studied and distance-optimal subfield codes over $\gf(p)$ were obtained, where $q=p^m$. The key idea for obtaining very good…
We define multi-block interleaved codes as codes that allow reading information from either a small sub-block or from a larger full block. The former offers faster access, while the latter provides better reliability. We specify the…
In the field of algebraic geometric codes (AG codes), the characterization of dual codes has long been a challenging problem which relies on differentials. In this paper, we provide some descriptions for certain differentials utilizing…
We consider the construction of maximal families of polynomials over the finite field $\mathbb{F}_q$, all having the same degree $n$ and a nonzero constant term, where the degree of the GCD of any two polynomials is $d$ with $1 \le d\le n$.…
Let $\mathbb{F}_q$ be a finite field with $q=p^{e}$ elements, where $p$ is a prime number and $e \geq 1$ is an integer. In this paper, by means of generalized Reed-Solomon (GRS) codes, we construct two new classes of quantum…
Lifted Reed-Solomon codes, a subclass of lifted affine-invariant codes, have been shown to be of high rate while preserving locality properties similar to generalized Reed-Muller codes, which they contain as subcodes. This work introduces a…