Related papers: Bounds for Batch Codes with Restricted Query Size
We prove a new lower bound for the unitary synthesis problem in the so-called 1.5-query setting. Our analysis establishes that any attempt to implement arbitrary n-qubit unitaries via limited oracle access requires resources that exceed the…
Additive codes may have better parameters than linear codes. However, still very few cases are known and the explicit construction of such codes is a challenging problem. Here we show that a Griesmer type bound for the length of additive…
We develop upper bounds on code size for an independent and identically distributed deletion and insertion channels for a given code length and target frame error probability. The bounds are obtained as a variation of a general converse…
Bounds on the entropy of patterns of sequences generated by independently identically distributed (i.i.d.) sources are derived. A pattern is a sequence of indices that contains all consecutive integer indices in increasing order of first…
We apply polynomial techniques (linear programming) to obtain lower and upper bounds on the covering radius of spherical designs as function of their dimension, strength, and cardinality. In terms of inner products we improve the lower…
In this paper q-ary Raptor codes under ML decoding are considered. An upper bound on the probability of decoding failure is derived using the weight enumerator of the outer code, or its expected weight enumerator if the outer code is drawn…
LDPC codes play a vital role in coding theory and practical error correction. A central problem in this direction is to understand their rate--distance tradeoff. In this paper, we introduce a new framework for estimating ball sizes in the…
We present some variations affecting the association measure and thresholding on a technique for learning Selectional Restrictions from on-line corpora. It uses a wide-coverage noun taxonomy and a statistical measure to generalize the…
We demonstrate propagation rules of subsystem code constructions by extending, shortening and combining given subsystem codes. Given an $[[n,k,r,d]]_q$ subsystem code, we drive new subsystem codes with parameters $[[n+1,k,r,\geq d]]_q$,…
We present new lower and upper bounds for the compression rate of binary prefix codes optimized over memoryless sources according to two related exponential codeword length objectives. The objectives explored here are exponential-average…
Upper bounds are derived for codes in Stiefel and Grassmann manifolds with given minimal chordal distance. They stem from upper bounds for codes in products of unit spheres and projective spaces. The new bounds are asymptotically better…
Error-correcting codes resilient to synchronization errors such as insertions and deletions are known as insdel codes. Due to their important applications in DNA storage and computational biology, insdel codes have recently become a focal…
In an application, where a client wants to obtain many elements from a large database, it is often desirable to have some load balancing. Batch codes (introduced by Ishai et al. in STOC 2004) make it possible to do exactly that: the large…
Locally repairable codes (LRCs) have gained significant interest for the design of large distributed storage systems as they allow a small number of erased nodes to be recovered by accessing only a few others. Several works have thus been…
This paper computationally obtains optimal bounded-weight, binary, error-correcting codes for a variety of distance bounds and dimensions. We compare the sizes of our codes to the sizes of optimal constant-weight, binary, error-correcting…
One of the main problems of the research area of network coding is to compute good lower and upper bounds of the achievable cardinality of so-called subspace codes in $\operatorname{PG}(n,q)$, i.e., the set of subspaces of $\mathbb{F}_q^n$,…
Alphabetic codes and binary search trees are combinatorial structures that abstract search procedures in ordered sets endowed with probability distributions. In this paper, we design new linear-time algorithms to construct alphabetic codes,…
Learned index structures aim to accelerate queries by training machine learning models to approximate the rank function associated with a database attribute. While effective in practice, their theoretical limitations are not fully…
Finding the largest code with a given minimum distance is one of the most basic problems in coding theory. In this paper, we study the linear programming bound for codes in the Lee metric. We introduce refinements on the linear programming…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. In the context of a branch-and-bound framework for solving these packing problems to optimality, it is…