Related papers: Bounds and Constructions for $\overline{3}$-Strong…
A circulant-based spatially-coupled (SC) code is constructed by partitioning the circulants of an underlying block code into a number of components, and then coupling copies of these components together. By connecting (coupling) several SC…
Consider a $q$-ary block code satisfying the property that no $l$-letters long codeword's prefix occurs as a suffix of any codeword for $l$ inside some interval. We determine a general upper bound on the maximum size of these codes and a…
Large language models face significant computational bottlenecks during inference due to the expensive output layer computation over large vocabularies. We present CSV-Decode, a novel approach that uses geometric upper bounds to construct…
Subspace codes are the $q$-analog of binary block codes in the Hamming metric. Here the codewords are vector spaces over a finite field. They have e.g. applications in random linear network coding, distributed storage, and cryptography. In…
Strongly multiplicative linear secret sharing schemes (LSSS) have been a powerful tool for constructing secure multiparty computation protocols. However, it remains open whether or not there exist efficient constructions of strongly…
Binary multimedia identifiable parent property codes (binary $t$-MIPPCs) are used in multimedia fingerprinting schemes where the identification of users taking part in the averaging collusion attack to illegally redistribute content is…
We present a case for the use of codes possessing algebraic closure properties - coset codes - in developing coding techniques and characterizing achievable rate regions for generic multi-terminal channels. In particular, we consider three…
In this paper, we study upper bounds on the minimum length of frameproof codes introduced by Boneh and Shaw to protect copyrighted materials. A $q$-ary $(k,n)$-frameproof code of length $t$ is a $t \times n$ matrix having entries in…
Modern dense Flash memory devices operate at very low error rates, which require powerful error correcting coding (ECC) techniques. An emerging class of graph-based ECC techniques that has broad applications is the class of…
We prove that for every odd $q\geq 3$, any $q$-query binary, possibly non-linear locally decodable code ($q$-LDC) $E:\{\pm1\}^k \rightarrow \{\pm1\}^n$ must satisfy $k \leq \tilde{O}(n^{1-2/q})$. For even $q$, this bound was established in…
Optical orthogonal signature pattern codes (OOSPCs) have attracted wide attention as signature patterns of spatial optical code division multiple access networks. In this paper, an improved upper bound on the size of an…
We study the secure decentralized Pliable Index CODing (PICOD) problem with circular side information sets at the users. The security constraint forbids every user to decode more than one message while a decentralized setting means there is…
The surface code is a two-dimensional topological code with code parameters that scale optimally with the number of physical qubits, under the constraint of two-dimensional locality. In three spatial dimensions an analogous simple yet…
A superimposed code is a collection of binary vectors (codewords) with the property that no vector is contained in the Boolean sum of any $k$ others, enabling unique identification of codewords within any group of $k$. Superimposed codes…
Because of their capacity-approaching performance and their complexity/latency advantages, spatially-coupled (SC) codes are among the most attractive error-correcting codes for use in modern dense data storage systems. SC codes are…
A variable-length code is a fix-free code if no codeword is a prefix or a suffix of any other codeword. In a fix-free code any finite sequence of codewords can be decoded in both directions, which can improve the robustness to channel noise…
The color code is a topological quantum error-correcting code supporting a variety of valuable fault-tolerant logical gates. Its two-dimensional version, the triangular color code, may soon be realized with currently available…
The mds (maximum distance separable) conjecture claims that a nontrivial linear mds $[n,k]$ code over the finite field $GF(q)$ satisfies $n \leq (q + 1)$, except when $q$ is even and $k = 3$ or $k = q- 1$ in which case it satisfies $n \leq…
Emerging applications in manufacturing, wireless communication, and molecular data storage require robust coding schemes that remain effective under physical distortions where codewords may be arbitrarily fragmented and partially missing.…
Recent work by Divsalar et al. has shown that properly designed protograph-based low-density parity-check (LDPC) codes typically have minimum (Hamming) distance linearly increasing with block length. This fact rests on ensemble arguments…