arXiv subjects

Myong-Son Sin

Publications and source records attributed to Myong-Son Sin.

3 recordsLinked to original sources

arXiv2014

Swan-like reducibility for Type I pentanomials over a binary field

Swan (Pacific J. Math. 12(3) (1962), 1099-1106) characterized the parity of the number of irreducible factors of trinomials over $F_2$. Many researchers have recently obtained Swan-like results on determining the reducibility of polynomials over finite fields. In this paper, we determine the parity of the number of irreducible factors for so-called Type I pentanomial $f(x)=x^m+x^{n+1}+x^n+x+1$ over $F_2$ with even $n$. Our result is based on the Stickelberger-Swan theorem and Newton's formula which is very useful for the computation of the discriminant of a polynomial.

math.RA↗

arXiv2013

Upper Bounds on the Number of Codewords of Some Separating Codes

Separating codes have their applications in collusion-secure fingerprinting for generic digital data, while they are also related to the other structures including hash family, intersection code and group testing. In this paper we study upper bounds for separating codes. First, some new upper bound for restricted separating codes is proposed. Then we illustrate that the Upper Bound Conjecture for separating Reed-Solomon codes inherited from Silverberg's question holds true for almost all Reed-Solomon codes.

cs.IT↗

arXiv2013

Some New Results on Equivalency of Collusion-Secure Properties for Reed-Solomon Codes

A. Silverberg (IEEE Trans. Inform. Theory 49, 2003) proposed a question on the equivalence of identifiable parent property and traceability property for Reed-Solomon code family. Earlier studies on Silverberg's problem motivate us to think of the stronger version of the question on equivalence of separation and traceability properties. Both, however, still remain open. In this article, we integrate all the previous works on this problem with an algebraic way, and present some new results. It is notable that the concept of subspace subcode of Reed-Solomon code, which was introduced in error-correcting code theory, provides an interesting prospect for our topic.

cs.IT↗