Perfect Codes and Balanced Generalized Weighing Matrices, II
نویسندگان
چکیده
منابع مشابه
Balanced Generalized Weighing Matrices and their Applications
Balanced generalized weighing matrices include well-known classical combinatorial objects such as Hadamard matrices and conference matrices; moreover, particular classes of BGW -matrices are equivalent to certain relative difference sets. BGW -matrices admit an interesting geometrical interpretation, and in this context they generalize notions like projective planes admitting a full elation or ...
متن کاملApplying Balanced Generalized Weighing Matrices to Construct Block Designs
Balanced generalized weighing matrices are applied for constructing a family of symmetric designs with parameters (1 + qr(rm+1 − 1)/(r − 1), rm, rm−1(r − 1)/q), where m is any positive integer and q and r = (qd − 1)/(q − 1) are prime powers, and a family of non-embeddable quasi-residual 2−((r+1)(rm+1−1)/(r−1), rm(r+ 1)/2, rm(r− 1)/2) designs, where m is any positive integer and r = 2d− 1, 3 · 2...
متن کاملWeighing matrices and spherical codes
Mutually unbiased weighing matrices (MUWM) are closely related to an antipodal spherical code with 4 angles. In this paper, we clarify the relation between MUWM and the spherical codes, and determine the maximum size of a set of MUWM with weight 4 for any order. Moreover, we define mutually quasi-unbiased weighing matrices (MQUWM) as a natural generalization of MUWM from the viewpoint of spheri...
متن کاملGeneralized Reed-Solomon Codes with Sparsest and Balanced Generator Matrices
We prove that for any positive integers n and k such that n≥ k≥ 1, there exists an [n, k] generalized Reed-Solomon (GRS) code that has a sparsest and balanced generator matrix (SBGM) over any finite field of size q ≥ n+ ⌈ k(k−1) n ⌉, where sparsest means that each row of the generator matrix has the least possible number of nonzeros, while balanced means that the number of nonzeros in any two c...
متن کاملOn Perfect Graphs and Balanced Matrices
I would like to thank my advisor, Gerard Cornuéjols, for his support and his precious guidance. I also want to express my gratitude towards Michele Conforti, who introduced me to the field of combinatorics when I has an undergraduate student in Padova, and encouraged me to continue. Several parts of this dissertation resulted from working jointly with Michele Con-forti, Gerard Cornuéjols, and K...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2002
ISSN: 1071-5797
DOI: 10.1006/ffta.2001.0327