Related papers: Constructive spherical codes near the Shannon boun…
We present two constructions for binary self-orthogonal codes. It turns out that our constructions yield a constructive bound on binary self-orthogonal codes. In particular, when the information rate R=1/2, by our constructive lower bound,…
For $q,n,d \in \mathbb{N}$, let $A_q^L(n,d)$ denote the maximum cardinality of a code $C \subseteq \mathbb{Z}_q^n$ with minimum Lee distance at least $d$, where $\mathbb{Z}_q$ denotes the cyclic group of order $q$. We consider a…
The task of constructing infinite families of self-dual codes with unbounded lengths and minimum distances exhibiting square-root lower bounds is extremely challenging, especially when it comes to cyclic codes. Recently, the first infinite…
We study a construction of Quantum LDPC codes proposed by MacKay, Mitchison and Shokrollahi. It is based on the Cayley graph of Fn together with a set of generators regarded as the columns of the parity-check matrix of a classical code. We…
Over any discrete memoryless channel, we build codes such that: for one, their block error probabilities and code rates scale like random codes'; and for two, their encoding and decoding complexities scale like polar codes'. Quantitatively,…
Non-overlapping codes have been studied for almost 60 years. In such a code, no proper, non-empty prefix of any codeword is a suffix of any codeword. In this paper, we study codes in which overlaps of certain specified sizes are forbidden.…
The additive codes may have better parameters than linear codes. However, it is still a challenging problem to efficiently construct additive codes that outperform linear codes, especially those with greater distances than linear codes of…
We consider linear cyclic codes with the locality property, or locally recoverable codes (LRC codes). A family of LRC codes that generalize the classical construction of Reed-Solomon codes was constructed in a recent paper by I. Tamo and A.…
A new class of space time codes with high performance is presented. The code design utilizes tailor-made permutation codes, which are known to have large minimal distances as spherical codes. A geometric connection between spherical and…
Classical BCH codes that contain their (Euclidean or Hermitian) dual codes can be used to construct quantum stabilizer codes; this correspondence studies the properties of such codes. It is shown that a BCH code of length n can contain its…
We investigate weakly constrained codes, in which specific patterns occur with prescribed frequencies rather than being strictly forbidden as in conventional constrained coding. We propose a capacity-achieving construction of a weakly…
Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are valid for a large class of potential functions. Our lower bounds…
In this paper, the authors provide a weak decoding version of the traditional source coding theorem of Claude Shannon. The central bound that is obtained is \[ \chi>\log_{\epsilon}(2^{-n(H(X)+\epsilon)}) \] where \[…
We consider the coding problem in the Stiefel manifold with chordal distance. After considering various low-dimensional instances of this problem, we use Rankin's bounds on spherical codes to prove upper bounds on the minimum distance of a…
In this note, we apply some techniques developed in [1]-[3] to give a particular construction of bivariate Abelian Codes from cyclic codes, multiplying their dimension and preserving their apparent distance. We show that, in the case of…
Spinal codes, a family of rateless codes introduced in 2011, have been proved to achieve Shannon capacity over both the additive white Gaussian noise (AWGN) channel and the binary symmetric channel (BSC). In this paper, we derive explicit…
Binary self-dual cyclic codes have been studied since the classical work of Sloane and Thompson published in IEEE Trans. Inf. Theory, vol. 29, 1983. Twenty five years later, an infinite family of binary self-dual cyclic codes with lengths…
The problem of channel code design for the $M$-ary input AWGN channel with additive $Q$-ary interference where the sequence of i.i.d. interference symbols is known causally at the encoder is considered. The code design criterion at high SNR…
Let $W$ be a binary-input memoryless symmetric (BMS) channel with Shannon capacity $I(W)$ and fix any $\alpha > 0$. We construct, for any sufficiently small $\delta > 0$, binary linear codes of block length $O(1/\delta^{2+\alpha})$ and rate…
In an interesting paper Professor Cunsheng Ding provided three constructions of cyclic codes of length being a product of two primes. Numerical data shows that many codes from these constructions are best cyclic codes of the same length and…