Combinatorial Codes 94

Combinatorial Codes 94 B 25

Regular low-density parity-check codes from combinatorial designs

Analytically constructed LDPC codes comprise only a very small subset of possible codes and as a result LDPC codes are still, for the most part, constructed randomly. This paper extends the class of LDPC codes that can be systematically generated by presenting a construction method for regular LDPC codes based on combinatorial designs known as Kirkman triple systems. We construct -codes whose T...

Combinatorial Characterizations of Authentication Codes

In this paper, we prove two new combinatorial characterizations of authentication codes. Authentication codes without secrecy are characterized in terms of orthogonal arrays; and general authentication codes are characterized in terms of balanced incomplete block designs.

Combinatorial batch codes and transversal matroids

Combinatorial batch codes were defined by Paterson, Stinson, and Wei as purely combinatorial versions of the batch codes introduced by Ishai, Kushilevitz, Ostrovsky, and Sahai. There are n items and m servers each of which stores a subset of the items. It is required that, for prescribed integers k and t, any k items can be retrieved by reading at most t items from each server. Only the case t ...

Specification of Neuronal Identities by Feedforward Combinatorial Coding

Neuronal specification is often seen as a multistep process: earlier regulators confer broad neuronal identity and are followed by combinatorial codes specifying neuronal properties unique to specific subtypes. However, it is still unclear whether early regulators are re-deployed in subtype-specific combinatorial codes, and whether early patterning events act to restrict the developmental poten...