Related papers: Query-Efficient Locally Decodable Codes of Subexpo…
We initiate the probabilistic analysis of linear programming (LP) decoding of low-density parity-check (LDPC) codes. Specifically, we show that for a random LDPC code ensemble, the linear programming decoder of Feldman et al. succeeds in…
This paper presents approaches to develop efficient network for non-binary quasi-cyclic LDPC (QC-LDPC) decoders. By exploiting the intrinsic shifting and symmetry properties of the check matrices, significant reduction of memory size and…
The coding theorem for Kolmogorov complexity states that any string sampled from a computable distribution has a description length close to its information content. A coding theorem for resource-bounded Kolmogorov complexity is the key to…
We provide a tight analysis of Grover's recent algorithm for quantum database searching. We give a simple closed-form formula for the probability of success after any given number of iterations of the algorithm. This allows us to determine…
Let $p$ be an odd prime and $r,s,m$ be positive integers. In this study, we initiate our exploration by delving into the intricate structure of all repeated-root cyclic codes and their duals with a length of $2^rp^s$ over the finite field…
This paper uses the reconstruction-computation-quantization (RCQ) paradigm to decode low-density parity-check (LDPC) codes. RCQ facilitates dynamic non-uniform quantization to achieve good frame error rate (FER) performance with very low…
This paper shows that, if we could examine the entire history of a hidden variable, then we could efficiently solve problems that are believed to be intractable even for quantum computers. In particular, under any hidden-variable theory…
We wish to generate list-decodable codes over small alphabets using as little randomness as possible. Specifically, we hope to generate codes achieving what we term the Elias bound, which means that they are $(\rho,L)$-list-decodable with…
Thin Lie algebras are Lie algebras L, graded over the positive integers, with all homogeneous components of dimension at most two, and satisfying a more stringent but natural narrowness condition modeled on an analogous one for pro-p…
Search queries with superlatives (e.g., best, most popular) require comparing candidates across multiple dimensions, demanding linguistic understanding and domain knowledge. We show that LLMs can uncover latent intent behind these…
Motivated by their research on automorphism groups of pseudo-real Riemann surfaces, Bujalance, Cirre and Conder have conjectured that there are infinitely many primes $p$ such that $p+2$ has all its prime factors $q\equiv -1$ mod~$(4)$. We…
We study privacy-preserving query answering in Description Logics (DLs). Specifically, we consider the approach of controlled query evaluation (CQE) based on the notion of instance indistinguishability. We derive data complexity results for…
We present a special-purpose algorithm for factoring semiprimes $N = pq$ in which one prime factor satisfies $p \approx c\,(a/b)^n$ for positive integers $a, b, c, n$ with $a > b$ and $\gcd(a,b) = 1$. Given the correct parameters $(a, b)$,…
In the SEARCH WITH ADVICE problem, a single entry of interest within a database of N entries is to be found assuming that an ordering of the entries, from that with the highest probability of being the entry of interest (as determined by a…
Quantum LDPC codes may provide a path to build low-overhead fault-tolerant quantum computers. However, as general LDPC codes lack geometric constraints, na\"ive layouts couple many distant qubits with crossing connections which could be…
Zeckendorf's theorem states that every positive integer can be written uniquely as the sum of non-consecutive shifted Fibonacci numbers $\{F_n\}$, where we take $F_1=1$ and $F_2=2$. This has been generalized for any Positive Linear…
Pr\"{u}fer domains and subclasses of integral domains such as Dedekind domains admit characterizations by means of the properties of their ideal lattices. Interestingly, a Leavitt path algebra $L$, in spite of being non-commutative and…
For $q$ a prime power, the discrete logarithm problem (DLP) in $\mathbb{F}_{q}$ consists in finding, for any $g \in \mathbb{F}_{q}^{\times}$ and $h \in \langle g \rangle$, an integer $x$ such that $g^x = h$. We present an algorithm for…
Nowadays, data is represented by vectors. Retrieving those vectors, among millions and billions, that are similar to a given query is a ubiquitous problem, known as similarity search, of relevance for a wide range of applications.…
We construct the q-discrete Painleve I and II equations and their higher order analogues by virtue of periodic cluster algebras. Using particular (k,k) exchange matrices, we show that the cluster algebras corresponding to k=4 and 5 give the…