Locally Decodable codes(LDC) support decoding of any particular symbol of the input message by reading constant number of symbols of the codeword, even in presence of constant fraction of errors. In a recent breakthrough [9], Yekhanin constructed 3-query LDCs that hugely improve over earlier constructions. Specifically, for a Mersenne prime p = 2−1, binary LDCs of length 2O(n1/t) for infinitely...

The classical Mersenne problem has been a stimulating challenge to number theorists and computer scientists for many years. After briefly reviewing some of the natural settings in which this problem appears as a special case, we introduce an analogue of the Mersenne problem in higher rank, in both a classical and an elliptic setting. Numerical evidence is presented for both cases, and some of t...

If p is prime, Mp = 2P — 1 is called a Mersenne number. If ui = 4 and «<+1 = Mj+i — 2, then M„ is prime if and only if uv-i m 0(mod Mp). This is called the Lucas test (see Lehmer [4]). The primes Mom , M mi, and Mu2W which are now the largest known primes, were discovered by Illiac II at the Digital Computer Laboratory of the University of Illinois. The computing times were 1 hour 23 minutes, 1...

Pseudo-random numbers with long periods and good statistical properties are often required for applications in computational finance. We consider the requirements for good uniform random number generators, and describe a class of generators whose period is a Mersenne prime or a small multiple of a Mersenne prime. These generators are based on “almost primitive” trinomials, that is trinomials ha...

MT19937 is a kind of Mersenne Twister, which is a pseudo-random number generator. This study presents new designs for a MT19937 circuit suitable for custom computing machinery for highperformance scientific simulations. Our designs can generate multiple random numbers per cycle (multi-port design). The estimated throughput of a 52-port design was 262Gbps, which is 115 times higher than the soft...

Pseudorandom number generators are widely used in the area of simulation. Defective generators are still widely used in standard library programs, although better pseudorandom number generators such as the Mersenne Twister are freely avail-

Fast uniform random number generators with extremely long periods have been defined and implemented based on linear recurrences modulo 2. The twisted GFSR and the Mersenne twister are famous recent examples. Besides the period length, the statistical quality of these generators is usually assessed via their equidistribution properties. The huge-period generators proposed so far are not quite op...