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1 Abbreviations and Notations 2 A Note for the Reader 3
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Research Interests: Geography, Mathematics, Computer Science, Combinatorics, Philosophy of Property, and 13 morePure Mathematics, Discrete Mathematics, Orthogonal Array, Alphabet, Linear Code, See, Upper Bound, Cohen, Faculty Department of Mathematics Faculty of Science, Copyright Protection, Orthogonal Arrays, Error Correction Code, and Descendant
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Research Interests: Mathematics, Computer Science, Space Technology, Algorithm, Coding, and 13 moreDiscrete Mathematics, Network coding, Design Methodology, Skeleton, Decoding, Linear Code, Galois Fields, Metric, Electrical And Electronic Engineering, Reduced row echelon form, Code Block, Error Correction Code, and projective space
Research Interests: Mathematics, Computer Science, Economics, Remote Sensing, Combinatorics, and 15 moreCryptography, Electromagnetic Interference, Grid, Ems, Codes, Costas array, Lower Bound, Metric, Electrical And Electronic Engineering, Euclidean Distance, Key Distribution, Honeycomb structure, Costas arrays, Distance Measure, and Rectangle
A multiset combinatorial batch code (MCBC) over vector space consists of a set of subspaces of $\mathbb{F}_{q}^{n}$, each corresponding to a server, such that requests consisting of $t$ dimensional subspaces, can be retrieved from the... more
A multiset combinatorial batch code (MCBC) over vector space consists of a set of subspaces of $\mathbb{F}_{q}^{n}$, each corresponding to a server, such that requests consisting of $t$ dimensional subspaces, can be retrieved from the servers. The code is said to be regular if all the subspaces in the code have the same dimension. The aim is to find the minimum number of total storage, and also the minimum number of servers in the regular case, fixing other parameters. In this paper, we provide bounds and constructions for this new class of batch codes.
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ABSTRACT This paper studies the error linear complexity profiles of binary sequences with period 2n. We give a precise categorization of those sequences having 2 distinct critical points in their profiles, as well as an enumeration of... more
ABSTRACT This paper studies the error linear complexity profiles of binary sequences with period 2n. We give a precise categorization of those sequences having 2 distinct critical points in their profiles, as well as an enumeration of these sequences. We also give an upper bound on the maximum number of distinct critical points that the profile of a sequence can have, along with several constructions for sequences having many distinct critical points.
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An n×n array in which each of the symbols 1,2,...,n appears exactly once in each row is called an Italian square (a better name would be a row Latin square), and a Tuscan-k square is an Italian square with the additional property that for... more
An n×n array in which each of the symbols 1,2,...,n appears exactly once in each row is called an Italian square (a better name would be a row Latin square), and a Tuscan-k square is an Italian square with the additional property that for any two numbers a and b, and for each m with 1≤m≤k, there is at most one row in which b is the m-th symbol to the right of a. If the vertices of a regular n-gon are numbered 1,2,...,n in counterclockwise order, then by a polygonal path is meant a path which starts at one vertex, ends at another and proceeds along directed chords to visit each of the n vertices once. The authors discuss the existence of Tuscan-k squares via polygonal path constructions. They also include numerous examples as well as a list of 12 questions and the current state of affairs regarding each question.