Abstract Recently, Lovejoy introduced the construct of overpartition pairs which are a natural generalization of overpartitions. Here we generalize that idea to overpartition ktuples and prove several congruences related to them. We denote the number of overpartition k-tuples of a positive integer n by pk(n) and prove, for example, that for all n ≥ 0, pt−1(tn + r) ≡ 0 (mod t) where t is prime a...

Abstract. We prove two related concentration inequalities concerning the number of rational points of hyperelliptic curves over subsets of a finite field. In particular, we investigate the probability of a large discrepancy between the numbers of quadratic residues and non-residues in the image of such subsets over uniformly random hyperelliptic curves of given degrees. We find a constant proba...

In this paper, we introduce a new definitions of the Gray weight and the Gray map for linear codes over Z9+uZ9 with u 2 = u. Some results on self-dual codes over this ring are investigated. Further, the structural properties of quadratic residue codes are also considered. Two self-dual codes with parameters [22, 11, 5] and [24, 12, 9] over Z9 are obtained.

In this paper, a modification decoding algorithm for the (89, 45, 17) QR code is proposed to decode all error patterns with weight less than six and high percentage weight-6, weight-7, and weight-8 error patterns.

Binary optimal codes often contain optimal or near-optimal subcodes. In this paper we show that this is true for the family of self-dual codes. One approach is to compute the optimum distance profiles (ODPs) of linear codes, which was introduced by Luo, et. al. (2010). One of our main results is the development of general algorithms, called the Chain Algorithms, for finding ODPs of linear codes...

mulches often use for weed control, hold soil moisture, decrease soil temperature, soil fertility, soil conservation, soil against rain and soil quality in organic farming. a field experiment was conducted to evaluate the effect of different wheat residue and sunflower densities on sunflower growth and yield during 2007 growing season at the research field of birjand university. the experimenta...

Let G be the automorphism group of the four-dimensional cube, a group of order24 . 4 ! = 384. The binary codes associated with the 32-dimensional permutationrepresentation of G on the edges of the cube are investigated. There are about 400 suchcodes, one of which is a [32, 17, 8] code, having twice as many codewords as the[32, 16, 8] extended quadratic residue code. __________<l...

We consider the problem of finding a trellis for a finear block code that minimizes one or more measures of trellis complexity. The domain of optimization may be different permutations of the same code or different codes with the same parameters. Constraints on trellises, including relationships between the minimal trellis of a code and that of the dual code, are used to derive bounds on comple...

crop residue is a non-chemical method of weed control in agricultural sustainable systems. this research was conducted at the alarogh site of ardabilto evaluate the effect of integrated use of mulch and herbicide on weed emergence and growth in potato in 2007. treatments were four levels herbicide including: (1) paraquat [n,n&apos;-dimethyl-4,4&apos;-bipyridinium dichloride] herbicide as pre-pl...