A c-identifying residue-pair representation: sufficient conditions and application to c-secure crt code

We define a c-identifying representa- tion as a generalization of the c-IPP code, and de- rive sufficient conditions of residue-pair representation and residue-tuple representation to be c-identifying, re- spectively. We construct a variant of the c-secure CRT code by replacing the outer code with the c-identifying residue-pair representation, which has shorter code length than the original code for small c. I. INTRODUCTION We have proposed a c-secure CRT code (2), reducing the code length of the c-secure code with €-error (l). It has a concate- nated structure, and both the inner code and the outer code cause erroneous tracing. However, the probability of tracing error is bounded. In this paper, we provide a combinatorial outer code causing no tracing error. It is known that the c-IPP code causes no tracing error (3). The outer code of the c-secure CRT code is based on a slightly different marking assumption. Moreover, the c-IPP code is a uniform code, whereas the outer code is not. Because of these two differences, the known re- sult of the c-IPP code cannot be applied to the outer code straightforwardly. We consider a common generalization of the c-IPP code and the outer code of the c-secure CRT code. 11. C-IDENTIFYING REPRESENTATION