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Minimal blocking sets in have size at most . This result is due to Bruen and Thas and the bound is sharp, sets attaining this bound are called unitals. In this paper, we show that the second largest minimal blocking sets have size at most , if , , or , , . Our proof also works for sets having at least one tangent at each of its points (that is, for tangency sets). 相似文献
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We consider four classes of polynomials over the fields , , , , , , , where . We find sufficient conditions on the pairs for which these polynomials permute and we give lower bounds on the number of such pairs. 相似文献
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《Discrete Mathematics》2023,346(4):113304
In 1965 Erd?s asked, what is the largest size of a family of k-element subsets of an n-element set that does not contain a matching of size ? In this note, we improve upon a recent result of Frankl and resolve this problem for and . 相似文献
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Let M be a random rank-r matrix over the binary field , and let be its Hamming weight, that is, the number of nonzero entries of M.We prove that, as with r fixed and tending to a constant, we have that converges in distribution to a standard normal random variable. 相似文献
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《Discrete Mathematics》2024,347(1):113657
A frequency n-cube is an n-dimensional q-by-...-by-q array, where , filled by numbers with the property that each line contains exactly cells with symbol i, (a line consists of q cells of the array differing in one coordinate). The trivial upper bound on the number of frequency n-cubes is . We improve that lower bound for , replacing by a smaller value s, by constructing a testing set of size for frequency n-cubes (a testing set is a collection of cells of an array the values in which uniquely determine the array with given parameters). We also construct new testing sets for generalized frequency n-cubes, which are essentially correlation-immune functions in n q-valued arguments; the cardinalities of new testing sets are smaller than for testing sets known before. 相似文献
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In this paper, based on the structure of embedded fields, we investigate explicit construction of systematic mMDS sliding window codes with memory . First, over GF() with and , we propose an algorithm to construct mMDS codes with memory 2, which are optimal in the sense that is the maximum possible value of k for a sliding window code with memory 2 over GF() to be mMDS. When , every constructed code has the extra property that it contains a mMDS sliding window code with memory 2 as a subcode over the subfield GF(). Next, over GF() with and , we introduce a method to construct mMDS codes memory 3, and a few new codes have been obtained consequently. When , every code constructed by the new approach also has the property that it contains an mMDS subcode over the subfield GF(). The embedding subfield-subcode property enhances the flexibility and efficiency of the designed codes. 相似文献
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《Journal of Functional Analysis》2023,284(7):109835
We employ separation of variables to prove weighted resolvent estimates for the semiclassical Schrödinger operator in dimension , where , and is and compactly supported. The weighted resolvent norm grows no faster than , while an exterior weighted norm grows . We introduce a new method based on the Mellin transform to handle the two-dimensional case. 相似文献
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Cyclic code is an interesting topic in coding theory and communication systems. In this paper, we investigate the ternary cyclic codes with parameters based on some results proposed by Ding and Helleseth in 2013. Six new classes of optimal ternary cyclic codes are presented by determining the solutions of certain equations over . 相似文献
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In this paper, we give the dimension and the minimum distance of two subclasses of narrow-sense primitive BCH codes over with designed distance for all , where q is a prime power and is a positive integer. As a consequence, we obtain an affirmative answer to two conjectures proposed by C. Ding in 2015. Furthermore, using the previous part, we extend some results of Yue and Hu [16], and we give the dimension and, in some cases, the Bose distance for a large designed distance in the range for , where if m is odd, and if m is even. 相似文献
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After a brief review of the existing results on permutation binomials of finite fields, we introduce the notion of equivalence among permutation binomials (PBs) and describe how to bring a PB to its canonical form under equivalence. We then focus on PBs of of the form , where n and d are positive integers and . Our contributions include two nonexistence results: (1) If q is even and sufficiently large and , then is not a PB of . (2) If , q is sufficiently large and , then is not a PB of under certain additional conditions. (1) partially confirms a recent conjecture by Tu et al. (2) is an extension of a previous result with . 相似文献