Equivalence of Hadamard matrices and Pseudo-Noise matrices
نویسندگان
چکیده
Several classes of structured matrices (e.g., the Hadamard-Sylvester matrices and the pseudo-noise matrices) are used in the design of error-correcting codes. In particular, the columns of matrices belonging to the above two matrix classes are often used as codewords. In this paper we show that the two above classes essentially coincide: the pseudo-noise matrices can be obtained from the Hadamard-Sylvester matrices by means of the row/column permutations.
منابع مشابه
Ranks of Hadamard Matrices and Equivalence of Sylvester Hadamard and Pseudo-Noise Ma- trices
In this paper we obtain several results on the rank properties of Hadamard matrices (including Sylvester Hadamard matrices) as well as (generalized) Hadamard matrices. These results are used to show that the classes of (generalized) Sylvester Hadamard matrices and of generalized pseudo-noise matrices are equivalent, i.e., they can be obtained from each other by means of row/column permutations....
متن کاملOn the classification of Hadamard matrices of order 32
All equivalence classes of Hadamard matrices of order at most 28 have been found by 1994. Order 32 is where a combinatorial explosion occurs on the number of inequivalent Hadamard matrices. We find all equivalence classes of Hadamard matrices of order 32 which are of certain types. It turns out that there are exactly 13,680,757 Hadamard matrices of one type and 26,369 such matrices of another t...
متن کاملWeak log-majorization inequalities of singular values between normal matrices and their absolute values
This paper presents two main results that the singular values of the Hadamard product of normal matrices $A_i$ are weakly log-majorized by the singular values of the Hadamard product of $|A_{i}|$ and the singular values of the sum of normal matrices $A_i$ are weakly log-majorized by the singular values of the sum of $|A_{i}|$. Some applications to these inequalities are also given. In addi...
متن کاملAbout the code equivalence
In this paper, we consider the algorithm for equivalence which is implemented in the current version of the package Q − Extension [3]. Mainly, this package can be used for classification of linear codes over small fields. Actually, we reduce, as many other algorithms do, the equivalence test for linear codes to a test for isomorphism of binary matrices or bipartite graphs. This allows us to use...
متن کاملOn Classification of Generalized Hadamard Matrices
In this paper, we give an algorithm to list and classify generalized Hadamard matrices of a given order over an arbitrary elementary Abelian group. Generalized Hadamard matrices of order less than or equal to 16 over Abelian groups Z3; Z4, Z2 Z2 and Z5 have been classi ed up to equivalence. We have shown that generalized Hadamard matrices of order 4; 8, and 12 over EA(4) are unique up to equiva...
متن کامل