相关论文: Good traceability codes do exist

The locally repairable codes (LRCs) were introduced to correct erasures efficiently in distributed storage systems. LRCs are extensively studied recently. In this paper, we first deal with the open case remained in \cite{q} and derive an…

Non-fungible tokens (NFTs) are unique digital assets stored on the blockchain and is used to certify ownership and authenticity of the digital asset. NFTs were first created in 2014 while their popularity peaked between 2021 and 2022. In…

The strange attractor represents a complex pattern of behavior in dynamic systems. This paper introduces a strange attractor for synthetic channels in polar coding as a result of a geometric property of density evolution that is a polar…

Haah's cubic code is the prototypical type-II fracton topological order. It instantiates the no string-like operator property that underlies the favorable scaling of its code distance and logical energy barrier. Previously, the cubic code…

Let $q$ be a power of a prime $p$. In this paper, we study reversible cyclic codes of arbitrary length over the ring $ R = \mathbb{F}_q + u \mathbb{F}_q$, where $u^2=0 mod q$. First, we find a unique set of generators for cyclic codes over…

Can a list of binary strings be ordered so that consecutive strings differ in a single bit? Can a list of permutations be ordered so that consecutive permutations differ by a swap? Can a list of non-crossing set partitions be ordered so…

Let $\mathbb{F}_p$ denote the finite field of order $p$, where $p$ is an odd prime. We study certain quantum negacyclic codes over $\mathbb{F}_p$ which we call $t$-Frobenius negacyclic codes. We obtain a criterion for constructing such…

A linear code is said to be $\Delta$-divisible if the Hamming weights of all its codewords are divisible by $\Delta$. The $p$-adic valuation of a code is defined as the greatest integer $t$ such that the code is $p^t$-divisible. In this…

Quantum synchronizable codes are kinds of quantum error-correcting codes that can not only correct the effects of quantum noise on qubits but also the misalignment in block synchronization. In this paper, a new method for construct quantum…

Background: Establishing traceability from requirements documents to downstream artifacts early can be beneficial as it allows engineers to reason about requirements quality (e.g. completeness, consistency, redundancy). However, creating…

Batch codes are a useful notion of locality for error correcting codes, originally introduced in the context of distributed storage and cryptography. Many constructions of batch codes have been given, but few lower bound (limitation)…

An erasure code is said to be a code with sequential recovery with parameters $r$ and $t$, if for any $s \leq t$ erased code symbols, there is an $s$-step recovery process in which at each step we recover exactly one erased code symbol by…

An essential part of research and scientific communication is researchers' ability to reproduce the results of others. While there have been increasing standards for authors to make data and code available, many of these files are hard to…

Code clone detection is about finding out similar code fragments, which has drawn much attention in software engineering since it is important for software maintenance and evolution. Researchers have proposed many techniques and tools for…

Batch codes, introduced by Ishai, Kushilevitz, Ostrovsky and Sahai in [1], are methods for solving the following data storage problem: n data items are to be stored in m servers in such a way that any k of the n items can be retrieved by…

This paper studies fingerprinting (traitor tracing) games in which the number of colluders and the collusion channel are unknown. The fingerprints are embedded into host sequences representing signals to be protected and provide the…

A sequence $a=(a_n)_{n=1}^\infty$ of non-negative integers is called realizable if there is a self-map $T:X\to X$ on a set $X$ such that $a_n$ is equal to the number of periodic points of $T$ in $X$ of (not necessarily exact) period $n$,…

A code is locally recoverable when each symbol in one of its code words can be reconstructed as a function of $r$ other symbols. We use bundles of projective spaces over a line to construct locally recoverable codes with availability; that…

Locally repairable codes (LRCs) are a class of codes designed for the local correction of erasures. They have received considerable attention in recent years due to their applications in distributed storage. Most existing results on LRCs do…

Construction of capacity achieving deletion correcting codes has been a baffling challenge for decades. A recent breakthrough by Brakensiek $et~al$., alongside novel applications in DNA storage, have reignited the interest in this…