On very sparse circulant (0,1) matrices
نویسندگان
چکیده
منابع مشابه
Good Codes Based on Very Sparse Matrices
Unfortunately this paper contains two errors with respect to Gallager's work on low density parity check codes. We gained the impression from the literature that \the sparse parity check codes studied by Gallager are bad," but this is in fact not the case. We also had the impression that Gallager's decoding algorithm was the same as Meier and Staaelbach's, and that our use of belief propagation...
متن کاملOn circulant and two-circulant weighing matrices
We employ theoretical and computational techniques to construct new weighing matrices constructed from two circulants. In particular, we construct W (148, 144), W (152, 144), W (156, 144) which are listed as open in the second edition of the Handbook of Combinatorial Designs. We also fill a missing entry in Strassler’s table with answer ”YES”, by constructing a circulant weighing matrix of orde...
متن کاملOn Circulant Matrices
S ome mathematical topics—circulant matrices, in particular—are pure gems that cry out to be admired and studied with different techniques or perspectives in mind. Our work on this subject was originally motivated by the apparent need of the first author to derive a specific result, in the spirit of Proposition 24, to be applied in his investigation of theta constant identities [9]. Although pr...
متن کاملOn circulant weighing matrices
Algebraic techniques are employed to obtain necessary conditions for the existence of certain circulant weighing matrices. As an application we rule out the existence of many circulant weighing matrices. We study orders n = 8 +8+1, for 10 ~ 8 ~ 25. These orders correspond to the number of points in a projective plane of order 8.
متن کاملSingularity of Sparse Circulant Matrices is NP-complete
Abstract. It is shown by Karp reduction that deciding the singularity of (2 −1)× (2−1) sparse circulant matrices (SC problem) is NP-complete. We can write them only implicitly, by indicating values of the 2 + n(n + 1)/2 eventually nonzero entries of the first row and can make all matrix operations with them. The positions are 0, 1, 2 + 2. The complexity parameter is n. Mulmuley’s work on the ra...
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: Linear Algebra and its Applications
سال: 2006
ISSN: 0024-3795
DOI: 10.1016/j.laa.2006.02.029