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Secure codes are widely-studied combinatorial structures which were introduced for traitor tracing in broadcast encryption. To determine the maximum size of such structures is the main research objective. In this paper, we investigate the lower bounds for secure codes and their related structures. First, we give some improved lower bounds for the rates of $2$-frameproof codes and $overline{2}$-separable codes for slightly large alphabet size. Then we improve the lower bounds for the rate of some related structures, i.e., strongly $2$-separable matrices and $2$-cancellative set families. Finally, we give a general method to derive new lower bounds for strongly $t$-separable matrices and $t$-cancellative set families for $tge 3.$
An $(m,n,a,b)$-tensor code consists of $mtimes n$ matrices whose columns satisfy `$a$ parity checks and rows satisfy `$b$ parity checks (i.e., a tensor code is the tensor product of a column code and row code). Tensor codes are useful in distributed
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) results are know
This paper presents new lower and upper bounds for the compression rate of binary prefix codes optimized over memoryless sources according to various nonlinear codeword length objectives. Like the most well-known redundancy bounds for minimum average
The determination of weight distribution of cyclic codes involves evaluation of Gauss sums and exponential sums. Despite of some cases where a neat expression is available, the computation is generally rather complicated. In this note, we determine t
This paper considers the problem of secure coding design for a type II wiretap channel, where the main channel is noiseless and the eavesdropper channel is a general binary-input symmetric-output memoryless channel. The proposed secure error-correcti