Related papers: Optimal Narain CFTs from Codes
Ramanujan graphs are graphs whose spectrum is bounded optimally. Such graphs have found numerous applications in combinatorics and computer science. In recent years, a high dimensional theory has emerged. In this paper these developments…
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 give an exposition of some connections between Fourier optimization problems and problems in number theory. In particular, we present some recent conditional bounds under the generalized Riemann hypothesis, achieved via a Fourier…
A rateless code-i.e., a rate-compatible family of codes-has the property that codewords of the higher rate codes are prefixes of those of the lower rate ones. A perfect family of such codes is one in which each of the codes in the family is…
Let $A_q(n,d)$ be the maximum order (maximum number of codewords) of a $q$-ary code of length $n$ and Hamming distance at least $d$. And let $A(n,d,w)$ that of a binary code of constant weight $w$. Building on results from algebraic graph…
This paper investigates the problem of variable-length lossy source coding allowing a positive excess distortion probability and an overflow probability of codeword lengths. Novel one-shot achievability and converse bounds of the optimal…
Using the notion of generalized weight we improve estimates on the parameters of quantum codes obtained by Steane's construction from binary codes. This yields several new families of quantum codes.
We study a rich set of four-dimensional $\mathcal{N}=1$ superconformal field theories (SCFTs) with both central charges identical: $a = c$. We construct them via the diagonal $\mathcal{N}=1$ gauging of the flavor symmetry $G$ of a…
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…
Constant-dimension codes have recently received attention due to their significance to error control in noncoherent random linear network coding. What the maximal cardinality of any constant-dimension code with finite dimension and minimum…
A new family of binary linear completely transitive (and, therefore, completely regular) codes is constructed. The covering radius of these codes is growing with the length of the code. In particular, for any integer r > 1, there exist two…
We give two methods for constructing many linear complementary dual (LCD for short) codes from a given LCD code, by modifying some known methods for constructing self-dual codes. Using the methods, we construct binary LCD codes and…
We consider the problem of designing optimal linear codes (in terms of having the largest minimum distance) subject to a support constraint on the generator matrix. We show that the largest minimum distance can be achieved by a subcode of a…
We draw a new connection between Coppersmith's method for finding small solutions to polynomial congruences modulo integers and the capacity theory of adelic subsets of algebraic curves. Coppersmith's method uses lattice basis reduction to…
Progress in designing channel codes has been driven by human ingenuity and, fittingly, has been sporadic. Polar codes, developed on the foundation of Arikan's polarization kernel, represent the latest breakthrough in coding theory and have…
This study investigates imposing hard inequality constraints on the outputs of convolutional neural networks (CNN) during training. Several recent works showed that the theoretical and practical advantages of Lagrangian optimization over…
Given any polynomial system with fixed monomial term structure, we give explicit formulae for the generic number of roots with specified coordinate vanishing restrictions. For the case of affine space minus an arbitrary union of coordinate…
A new approach for upper bounding the channel reliability function using the code spectrum is described. It allows to treat in a unified way both a low and a high rate cases. In particular, the earlier known upper bounds are improved, and a…
We propose a new monotonically convergent algorithm which can enforce spectral constraints on the control field (and extends to arbitrary filters). The procedure differs from standard algorithms in that at each iteration the control field…
Conflict-avoiding codes (CACs) have been used in multiple-access collision channel without feedback. The size of a CAC is the number of potential users that can be supported in the system. A code with maximum size is called optimal. The use…