Related papers: Coding Theory using Linear Complexity of Finite Se…
In this work, we study the computational complexity of the Minimum Distance Code Detection problem. In this problem, we are given a set of noisy codeword observations and we wish to find a code in a set of linear codes $\mathcal{C}$ of a…
A practical measure for the complexity of sequences of symbols (``strings'') is introduced that is rooted in automata theory but avoids the problems of Kolmogorov-Chaitin complexity. This physical complexity can be estimated for ensembles…
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…
In this work, we study the codes over the integers with locality constraints. We introduce a weighted notion of locality over $\mathbb{Z}/q_1\mathbb{Z} \times \cdots \times \mathbb{Z}/q_n\mathbb{Z}$ and derive a Singleton-like bound for…
Classical computations can not capture the essence of infinite computations very well. This paper will focus on a class of infinite computations called convergent infinite computations}. A logic for convergent infinite computations is…
We derive a linear programming bound on the maximum cardinality of error-correcting codes in the sum-rank metric. Based on computational experiments on relatively small instances, we observe that the obtained bounds outperform all…
This paper deals with the problem of increasing the minimum distance of a linear code by adding one or more columns to the generator matrix. Several methods to compute extensions of linear codes are presented. Many codes improving the…
A large family of linear codes with flexible parameters from almost bent functions and perfect nonlinear functions are constructed and their parameters are determined. Some constructed linear codes and their related codes are optimal in the…
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…
Delsarte's method and its extensions allow to consider the upper bound problem for codes in 2-point-homogeneous spaces as a linear programming problem with perhaps infinitely many variables, which are the distance distribution. We show that…
Inspired by connections to two dimensional quantum theory, we define several models of computation based on permuting distinguishable particles (which we call balls), and characterize their computational complexity. In the quantum setting,…
This paper presents a new technique for disturbing the algebraic structure of linear codes in code-based cryptography. This is a new attempt to exploit Gabidulin codes in the McEliece setting and almost all the previous cryptosystems of…
In this paper, we provide two methods of constructing quantum codes from linear codes over finite chain rings. The first one is derived from the Calderbank-Shor-Steane (CSS) construction applied to self-dual codes over finite chain rings.…
The linear complexity and k-error linear complexity of a sequence have been used as important measures of keystream strength, hence designing a sequence with high linear complexity and $k$-error linear complexity is a popular research topic…
While concepts and tools from Theoretical Computer Science are regularly applied to, and significantly support, software development for discrete problems, Numerical Engineering largely employs recipes and methods whose correctness and…
In this paper, we propose a linear complexity encoding method for arbitrary LDPC codes. We start from a simple graph-based encoding method ``label-and-decide.'' We prove that the ``label-and-decide'' method is applicable to Tanner graphs…
We present an extension of known semidefinite and linear programming upper bounds for spherical codes. We apply the main result for the distance distribution of a spherical code and show that this method can work effectively In particular,…
Linear codes are widely studied in coding theory as they have nice applications in distributed storage, combinatorics, lattices, cryptography and so on. Constructing linear codes with desirable properties is an interesting research topic.…
As a research field of stream ciphers, the pursuit of a balance of security and practicality is the focus. The conditions for security usually have to satisfy at least high period and high linear complexity. Because the feedforward…
String matching is the problem of deciding whether a given $n$-bit string contains a given $k$-bit pattern. We study the complexity of this problem in three settings. Communication complexity. For small $k$, we provide near-optimal upper…