Related papers: New results for traitor tracing schemes
In this paper we investigate bounds on rate and minimum distance of codes with $t$ availability. We present bounds on minimum distance of a code with $t$ availability that are tighter than existing bounds. For bounds on rate of a code with…
Identifying and locating-dominating codes have been widely studied in circulant graphs of type $C_n(1,2, \ldots, r)$, which can also be viewed as power graphs of cycles. Recently, Ghebleh and Niepel (2013) considered identification and…
Frameproof codes are a class of secure codes introduced by Boneh and Shaw in the context of digital fingerprinting, and have been widely studied from a combinatorial point of view. In this paper, we study a quantitative extension of…
Various kinds of fingerprinting codes and their related combinatorial structures are extensively studied for protecting copyrighted materials. This paper concentrates on one specialised fingerprinting code named wide-sense frameproof codes…
A new bound on the minimum distance of q-ary cyclic codes is proposed. It is based on the description by another cyclic code with small minimum distance. The connection to the BCH bound and the Hartmann--Tzeng (HT) bound is formulated…
We present several generalizations of results for splitting authentication codes by studying the aspect of multi-fold security. As the two primary results, we prove a combinatorial lower bound on the number of encoding rules and a…
We study fundamental block-structured integer programs called tree-fold and multi-stage IPs. Tree-fold IPs admit a constraint matrix with independent blocks linked together by few constraints in a recursive pattern; and transposing their…
Goppa codes form an important class of alternant codes with wide applications in algebraic coding theory and code-based cryptography. Determining the true minimum distance of a Goppa code is a difficult problem. In this paper, we provide a…
This thesis makes several significant contributions to the theory of both Regenerating (RG) and Locally Recoverable (LR) codes. The two principal contributions are characterizing the optimal rate of an LR code designed to recover from $t$…
The non-local interactions in several quantum device architectures allow for the realization of more compact quantum encodings while retaining the same degree of protection against noise. Anticipating that short to medium-length codes will…
Let $C$ be a linear code of length $n$ and dimension $k$ over the finite field $\mathbb{F}_{q^m}$. The trace code $\mathrm{Tr}(C)$ is a linear code of the same length $n$ over the subfield $\mathbb{F}_q$. The obvious upper bound for the…
Parent-identifying schemes provide a way to identify causes from effects for some information systems such as digital fingerprinting and group testing. In this paper, we consider combinatorial structures for parent-identifying schemes.…
All codes with minimum distance 8 and codimension up to 14 and all codes with minimum distance 10 and codimension up to 18 are classified. Nonexistence of codes with parameters [33,18,8] and [33,14,10] is proved. This leads to 8 new exact…
In this paper, we construct a new family of distance-optimal binary cyclic codes with the minimum distance $6$ and a new family of distance-optimal quaternary cyclic codes with the minimum distance $4$. We also construct several families of…
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…
It has been established that when the gradient coding problem is distributed among $n$ servers, the computation load (number of stored data partitions) of each worker is at least $s+1$ in order to resists $s$ stragglers. This scheme incurs…
In this article, we propose a new construction of probabilistic collusion-secure fingerprint codes against up to three pirates and give a theoretical security evaluation. Our pirate tracing algorithm combines a scoring method analogous to…
The color code is both an interesting example of an exactly solved topologically ordered phase of matter and also among the most promising candidate models to realize fault-tolerant quantum computation with minimal resource overhead. The…
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)…
We address the maximum attainable rate of fingerprinting codes under the marking assumption, studying lower and upper bounds on the value of the rate for various sizes of the attacker coalition. Lower bounds are obtained by considering…