Related papers: A note on full weight spectrum codes
In this paper, we construct a large family of projective linear codes over ${\mathbb F}_{q}$ from the general simplicial complexes of ${\mathbb F}_{q}^m$ via the defining-set construction, which generalizes the results of [IEEE Trans. Inf.…
In this work, we determine new linear equations for the weight distribution of linear codes over finite chain rings. The identities are determined by counting the number of some special submatrices of the parity-check matrix of the code.…
Minimal codes are being intensively studied in last years. $[n,k]_{q}$-minimal linear codes are in bijection with strong blocking sets of size $n$ in $PG(k-1,q)$ and a lower bound for the size of strong blocking sets is given by…
The generalized Hamming weights (GHWs) of a linear code C extend the concept of minimum distance, which is the minimum cardinality of the support of all one-dimensional subspaces of C, to the minimum cardinality of the support of all…
A multifold $1$-perfect code ($1$-perfect code for list decoding) in any graph is a set $C$ of vertices such that every vertex of the graph is at distance not more than $1$ from exactly $\mu$ elements of $C$. In $q$-ary Hamming graphs,…
Complete complementary codes (CCCs) play a vital role not only in wireless communication, particularly in multicarrier systems where achieving an interference-free environment is of paramount importance, but also in the construction of…
The weight enumerators (quant-ph/9610040) of a quantum code are quite powerful tools for exploring its structure. As the weight enumerators are quadratic invariants of the code, this suggests the consideration of higher-degree polynomial…
A minimal code is a linear code where the only instance that a codeword has its support contained in the support of another codeword is when the codewords are scalar multiples of each other. Ashikhmin and Barg gave a sufficient condition…
Studying the generalized Hamming weights of linear codes is a significant research area within coding theory, as it provides valuable structural information about the codes and plays a crucial role in determining their performance in…
An important family of codes for data storage systems, cryptography, consumer electronics, and network coding for error control in digital communications are the so-called cyclic codes. This kind of linear codes are also important due to…
Let $\mathbb{F}_q$ be a finite field with $q$ elements and denote by $\theta : \mathbb{F}_q\to\mathbb{F}_q$ an automorphism of $\mathbb{F}_q$. In this paper, we deal with skew constacyclic codes, that is, linear codes of $\mathbb{F}_q^n$…
In this paper, we consider Griesmer codes, namely those linear codes meeting the Griesmer bound. Let $C$ be an $[n,k,d]_q$ Griesmer code with $q=p^f$, where $p$ is a prime and $f\ge1$ is an integer. In 1998, Ward proved that for $q=p$, if…
Subfield codes of linear codes over finite fields have recently received much attention. Some of these codes are optimal and have applications in secrete sharing, authentication codes and association schemes. In this paper, the $q$-ary…
The weight spectrum plays a crucial role in the performance of error-correcting codes. Despite substantial theoretical exploration of polar codes with mother code length, a framework for the weight spectrum of rate-compatible polar codes…
In this work, we study the Codeword Stabilized Quantum Codes (CWS codes) a generalization of the stabilizers quantum codes using a new approach, the algebraic structure of modules, a generalization of linear spaces. We show then a new…
In this paper, we study codes with sparse generator matrices. More specifically, low-density generator matrix (LDGM) codes with a certain constraint on the weight of the columns in the generator matrix are considered. In this paper, it is…
An $[n,k,d]$ linear code is said to be maximum distance separable (MDS) or almost maximum distance separable (AMDS) if $d=n-k+1$ or $d=n-k$, respectively. If a code and its dual code are both AMDS, then the code is said to be near maximum…
Self-dual binary linear codes have been extensively studied and classified for length n <= 40. However, little attention has been paid to linear codes that coincide with their orthogonal complement when the underlying inner product is not…
Linear codes with a few weights are very important in coding theory and have attracted a lot of attention. In this paper, we present a construction of $q$-ary linear codes from trace and norm functions over finite fields. The weight…
A cyclic codes of length $n$ over the rings $Z_{2^{m}}$ of integer of modulo $2^{m}$ is a linear code with property that if the codeword $(c_0,c_1,...,c_{n-1})\in \mathcal{C}$ then the cyclic shift $(c_1,c_2,...,c_0)\in \mathcal{C}$.…