Related papers: Constant-Weight and Constant-Charge Binary Run-Len…
Linear codes with a few weights can be applied to communication, consumer electronics and data storage system. In addition, the weight hierarchy of linear codes has many applications such as on the type II wire-tap channel, dealing with…
For the past decades, linear codes with few weights have been widely studied, since they have applications in space communications, data storage and cryptography. In this paper, a class of binary linear codes is constructed and their weight…
Run-Length Encoding (RLE) is one of the most fundamental tools in data compression. However, its compression power drops significantly if there lacks consecutive elements in the sequence. In extreme cases, the output of the encoder may…
Binary constant-weight codes have been extensively studied, due to both their numerous applications and to their theoretical significance. In particular, constant-weight codes have been proposed for error correction in store and forward. In…
A statistical estimation algorithm of the weight distribution of a linear code is shown, based on using its generator matrix as a compression function on random bit strings.
Random Linear Network Coding (RLNC) provides a theoretically efficient method for coding. Some of its practical drawbacks are the complexity of decoding and the overhead due to the coding vectors. For computationally weak and battery-driven…
Maximum run-length limited codes are constraint codes used in communication and data storage systems. Insertion/deletion correcting codes correct insertion or deletion errors caused in transmitted sequences and are used for combating…
We present a novel technique for encoding and decoding constant weight binary codes that uses a geometric interpretation of the codebook. Our technique is based on embedding the codebook in a Euclidean space of dimension equal to the weight…
A generic construction of linear codes over finite fields has recently received a lot of attention, and many one-weight, two-weight and three-weight codes with good error correcting capability have been produced with this generic approach.…
Run-length limited (RLL) codes are a well-studied class of constrained codes having application in diverse areas such as optical and magnetic data recording systems, DNA-based storage, and visible light communication. RLL codes have also…
Linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, several classes of $p$-ary linear codes with two or three weights are constructed…
Representing visual data using compact binary codes is attracting increasing attention as binary codes are used as direct indices into hash table(s) for fast non-exhaustive search. Recent methods show that ranking binary codes using…
We introduce the class of multiply constant-weight codes to improve the reliability of certain physically unclonable function (PUF) response. We extend classical coding methods to construct multiply constant-weight codes from known $q$-ary…
Binary linear codes with good parameters have important applications in secret sharing schemes, authentication codes, association schemes, and consumer electronics and communications. In this paper, we construct several classes of binary…
A constant weight binary code consists of $n$-bit binary codewords, each with exactly $w$ bits equal to 1, such that any two codewords are at least Hamming distance $d$ apart. $A(n,d,w)$ is the maximum size of a constant weight binary code…
We introduce a formula for determining the number of codewords of weight 2 in cyclic codes and provide results related to the count of codewords with weight 3. Additionally, we establish a recursive relationship for binary cyclic codes that…
Given two {0,1}-sequences X and Y of lengths m and n, respectively, we write L(X,Y) to denote the length of the longest common subsequence (LCS) of X and Y, and write L(m,n) to denote the expected value of L(X,Y) when X and Y are random…
From cosets of binary Hamming codes we construct diameter perfect constant-weight ternary codes with weight $n-1$ (where $n$ is the code length) and distances 3 and 5. The class of distance 5 codes has parameters unknown before. Keywords:…
This letter shows that linear Cellular Automata based on rules 90/150 generate all the solutions of linear difference equations with binary constant coefficients. Some of these solutions are pseudo-random noise sequences with application in…
Which integer sequences are sequences of generalized weights of a linear code? In this paper, we answer this question for linear block codes, rank-metric codes, and more generally for sum-rank metric codes. We do so under an existence…