Related papers: New Bounds For Frameproof Codes
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 the maximum length of $q$-ary codes as a function of alphabet size, code size, and Singleton defect. For an $(n, M, d)_q$ code with dimension $\kappa = \log_q M \ge 2$ and Singleton defect $s = n - \lceil\kappa\rceil + 1 - d$, we…
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…
We present a construction of 1-perfect binary codes, which gives a new lower bound on the number of such codes. We conjecture that this lower bound is asymptotically tight.
Minimal codewords have applications in decoding linear codes and in cryptography. We study the maximum number of minimal codewords in binary linear codes of a given length and dimension. Improved lower and upper bounds on the maximum number…
In a {\em locally recoverable} or {\em repairable} code, any symbol of a codeword can be recovered by reading only a small (constant) number of other symbols. The notion of local recoverability is important in the area of distributed…
A code is called a $q$-query locally decodable code (LDC) if there is a randomized decoding algorithm that, given an index $i$ and a received word $w$ close to an encoding of a message $x$, outputs $x_i$ by querying only at most $q$…
We consider a communication network where there exist wiretappers who can access a subset of channels, called a wiretap set, which is chosen from a given collection of wiretap sets. The collection of wiretap sets can be arbitrary. Secure…
As a crucial technique for integrated circuits (IC) test response compaction, $X$-compact employs a special kind of codes called $X$-codes for reliable compressions of the test response in the presence of unknown logic values ($X$s). From a…
This paper gives new methods of constructing {\it symmetric self-dual codes} over a finite field $GF(q)$ where $q$ is a power of an odd prime. These methods are motivated by the well-known Pless symmetry codes and quadratic double circulant…
For $q,n,d \in \mathbb{N}$, let $A_q(n,d)$ be the maximum size of a code $C \subseteq [q]^n$ with minimum distance at least $d$. We give a divisibility argument resulting in the new upper bounds $A_5(8,6) \leq 65$, $A_4(11,8)\leq 60$ and…
Minimal codes are linear codes where all non-zero codewords are minimal, i.e., whose support is not properly contained in the support of another codeword. The minimum possible length of such a $k$-dimensional linear code over $\mathbb{F}_q$…
The Johnson-type upper bound on the maximum size of a code of length $n$, distance $d=2w-1$ and constant composition ${\overline{w}}$ is $\lfloor\dfrac{n}{w_1}\rfloor$, where $w$ is the total weight and $w_1$ is the largest component of…
Binary $t$-frameproof codes ($t$-FPCs) are used in multimedia fingerprinting schemes where the identification of authorized users taking part in the averaging collusion attack is required. In this paper, a binary strongly…
Let $A(n,d,w)$ be the largest possible size of an $(n,d,w)$ constant-weight binary code. By adding new constraints to Delsarte linear programming, we obtain twenty three new upper bounds on $A(n,d,w)$ for $n \leq 28$. The used techniques…
Codes in finite projective spaces equipped with the subspace distance have been proposed for error control in random linear network coding. Here we collect the present knowledge on lower and upper bounds for binary subspace codes for…
Conflict-avoiding codes are used in the multiple-access collision channel without feedback. The number of codewords in a conflict-avoiding code is the number of potential users that can be supported in the system. In this paper, a new upper…
In this paper, we study the signature codes for weighted binary adder channel (WbAC) and collusion-resistant multimedia fingerprinting. Let $A(n,t)$ denote the maximum cardinality of a $t$-signature code of length $n$, and $A(n,w,t)$ denote…
For nonnegative integers $n,d,w$, let $A(n,d,w)$ be the maximum size of a code $C \subseteq \mathbb{F}_2^n$ with constant weight $w$ and minimum distance at least $d$. We consider two semidefinite programs based on quadruples of code words…
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…