Related papers: Connections Between Construction D and Related Con…
We obtain algorithmically effective versions of the dense lattice sphere packings constructed from orders in $\mathbb{Q}$-division rings by the first author. The lattices in question are lifts of suitable codes from prime characteristic to…
This paper consists of three parts. The first part presents a large class of new binary quasi-cyclic (QC)-LDPC codes with girth of at least 6 whose parity-check matrices are constructed based on cyclic subgroups of finite fields.…
The component-wise or Schur product $C*C'$ of two linear error correcting codes $C$ and $C'$ over certain finite field is the linear code spanned by all component-wise products of a codeword in $C$ with a codeword in $C'$. When $C=C'$, we…
We approximate $d$-variate periodic functions in weighted Korobov spaces with general weight parameters using $n$ function values at lattice points. We do not limit $n$ to be a prime number, as in currently available literature, but allow…
Neural network decoding algorithms are recently introduced by Nachmani et al. to decode high-density parity-check (HDPC) codes. In contrast with iterative decoding algorithms such as sum-product or min-sum algorithms in which the weight of…
We complete the building-up construction for self-dual codes by resolving the open cases over $GF(q)$ with $q \equiv 3 \pmod 4$, and over $\Z_{p^m}$ and Galois rings $\GR(p^m,r)$ with an odd prime $p$ satisfying $p \equiv 3 \pmod 4$ with…
In a recent paper, the authors have proved that for lattices A and B with zero, the isomorphism $Conc(A \otimes B)\cong Conc A \otimes Conc B$, holds, provided that the tensor product satisfies a very natural condition (of being…
This paper is motivated by the desire to study package management using the toolkit of the semantics of functional languages. As it transpires, this is deeply related to the semantics of concurrent computation. The models we produce are not…
The Plotkin construction combines two codes to a code of doubled length. It can be applied recursively. The class of Reed-Muller (RM) codes is a particular example. Also, a special class of generalized concatenated codes (GCC) can be…
Lattice-model simulations and experiments of some small proteins suggest that folding is essentially controlled by a few conserved contacts. Residues of these conserved contacts form the minimum set of native contacts needed to ensure…
In this paper, we propose the explicit construction of a new class of lattices based on polar codes, which are provably good for the additive white Gaussian noise (AWGN) channel. We follow the multilevel construction of Forney \textit{et…
The component-by-component construction is the standard method of finding good lattice rules or polynomial lattice rules for numerical integration. Several authors have reported that in numerical experiments the generating vector sometimes…
It was proved by Nill that for any lattice simplex of dimension $d$ with degree $s$ which is not a lattice pyramid, the inequality $d+1 \leq 4s-1$ holds. In this paper, we give a complete characterization of lattice simplices satisfying the…
A fundamental problem in coding theory is the design of an efficient coding scheme that achieves the capacity of the additive white Gaussian (AWGN) channel. The main objective of this short note is to point out that by concatenating a…
Binary matrix codes with restricted row and column weights are a desirable method of coded modulation for power line communication. In this work, we construct such matrix codes that are obtained as products of affine codes - cosets of…
We study error correcting codes that construct the Narain lattices of heterotic strings as code lattices. We identify, in both $E_8\times E_8$ and Spin$(32)/Z_2$ heterotic strings, a pair of a binary code and a set of the corresponding…
A construction is presented that allows to produce subspace codes of long length using subspace codes of shorter length in combination with a rank metric code. The subspace distance of the resulting code, called linkage code, is as good as…
An elementary combinatorial Tanner graph construction for a family of near-regular low density parity check codes achieving high girth is presented. The construction allows flexibility in the choice of design parameters like rate, average…
New quaternary Plotkin constructions are given and are used to obtain new families of quaternary codes. The parameters of the obtained codes, such as the length, the dimension and the minimum distance are studied. Using these constructions…
Our earlier article proved that if $n > 1$ translates of sublattices of $Z^d$ tile $Z^d$, and all the sublattices are Cartesian products of arithmetic progressions, then two of the tiles must be translates of each other. We re-prove this…