Related papers: Binary and Non-Binary Self-Dual Sequences and Maxi…
Recently, Byrnes presented a formula for the maximum length of a symmetric circuit code that has a long bit run and odd spread. Here we show that the formula is also valid when the spread is even. We also establish that all maximum length…
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. Perfect nonlinear monomials were employed to…
We study the construction of quasi-cyclic self-dual codes, especially of binary cubic ones. We consider the binary quasi-cyclic codes of length 3\ell with the algebraic approach of [9]. In particular, we improve the previous results by…
Some mutually quasi-unbiased weighing matrices are constructed from binary codes satisfying certain conditions. Motivated by this, in this note, we study binary codes satisfying the conditions. The weight distributions of binary codes…
In this paper, based on the nonbinary graph state, we present a systematic way of constructing good non-binary quantum codes, both additive and nonadditive, for systems with integer dimensions. With the help of computer search, which…
In this paper, we present a new bordered construction for self-dual codes which employs $\lambda$-circulant matrices. We give the necessary conditions for our construction to produce self-dual codes over a finite commutative Frobenius ring…
Maximum-length sequences (m-sequences for short) over finite fields are generated by linear feedback shift registers with primitive characteristic polynomials. These sequences have nice mathematical structures and good randomness properties…
Multi-dimensional cyclic code is a natural generalization of cyclic code. In an earlier paper we explored two-dimensional constacyclic codes over finite fields. Following the same technique, here we characterize the algebraic structure of…
Binary sequences with optimal autocorrelation play important roles in radar, communication, and cryptography. Finding new binary sequences with optimal autocorrelation has been an interesting research topic in sequence design.…
In this work, quadratic double and quadratic bordered double circulant constructions are applied to F_4 + uF_4 as well as F_4, as a result of which extremal binary self-dual codes of length 56 and 64 are obtained. The binary extension…
In the realm of rank-metric codes, Maximum Rank Distance (MRD) codes are optimal algebraic structures attaining the Singleton-like bound. A major open problem in this field is determining whether an MRD code can be extended to a longer one…
Orientable sequences, periodic sequences in which any $n$-tuple appears at most once in either direction, were introduced in the early 1990s for use in certain position location applications; constructions and upper bounds on the period for…
In this work, we study codes generated by elements that come from group matrix rings. We present a matrix construction which we use to generate codes in two different ambient spaces: the matrix ring $M_k(R)$ and the ring $R,$ where $R$ is…
In this paper, we introduce and investigate the neighborhood of binary self-dual codes. We prove that there is no better Type I code than the best Type II code of the same length. Further, we give some new necessary conditions for the…
Linear codes and $t$-designs are interactive with each other. It is well known that some $t$-designs have been constructed by using certain linear codes in recent years. However, only a small number of infinite families of the extended…
We study circuit codes with long bit runs (sequences of distinct transitions) and derive a formula for the maximum length for an infinite class of symmetric circuit codes with long bit runs. This formula also results in an improved lower…
A lot of attention has been paid to the investigation of the algebraic properties of linear codes. In most cases, this investigation involves the determination of required code automorphisms, which are useful for decoders, such as the…
Double polycirculant codes are introduced here as a generalization of double circulant codes. When the matrix of the polyshift is a companion matrix of a trinomial, we show that such a code is isodual, hence formally self-dual. Numerical…
We investigate binary sequences generated by non-Markovian rules with memory length $\mu$, similar to those adopted in Elementary Cellular Automata. This generation procedure is equivalente to a shift register and certain rules produce…
Sequences with low auto-correlation property have been applied in code-division multiple access communication systems, radar and cryptography. Using the inverse Gray mapping, a quaternary sequence of even length $N$ can be obtained from two…