TY - GEN

T1 - A note on classification of binary signal set in the view of Hadamard equivalence

AU - Park, Ki Hyeon

AU - Song, Hong Yeop

PY - 2009

Y1 - 2009

N2 - In this paper, we derive a kind of classification of binary signal set by adopting Hadamard equivalence of binary matrices. We propose a fast algorithm for checking the Hadamard equivalence for general binary matrices, and give an intuitive analysis on its time complexity. For this, we define Hadamard-equivalence on the set of binary matrices, and a function which induces a total order on them. With respect to this order relation, we define the minimal element which is used as a representative of an equivalence class. We applied the proposed algorithm to binary matrices of smaller sizes, and show the results. Finally, we discuss a new combinatorial problem of counting the number of and enumerating all the inequivalent binary minimal matrices of size m x n, and show the solutions for small sizes, leaving many of the observed properties as open problems.

AB - In this paper, we derive a kind of classification of binary signal set by adopting Hadamard equivalence of binary matrices. We propose a fast algorithm for checking the Hadamard equivalence for general binary matrices, and give an intuitive analysis on its time complexity. For this, we define Hadamard-equivalence on the set of binary matrices, and a function which induces a total order on them. With respect to this order relation, we define the minimal element which is used as a representative of an equivalence class. We applied the proposed algorithm to binary matrices of smaller sizes, and show the results. Finally, we discuss a new combinatorial problem of counting the number of and enumerating all the inequivalent binary minimal matrices of size m x n, and show the solutions for small sizes, leaving many of the observed properties as open problems.

UR - http://www.scopus.com/inward/record.url?scp=74549215023&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=74549215023&partnerID=8YFLogxK

U2 - 10.1109/IWSDA.2009.5346402

DO - 10.1109/IWSDA.2009.5346402

M3 - Conference contribution

AN - SCOPUS:74549215023

SN - 9781424443802

T3 - Proceedings of the 4th International Workshop on Signal Design and Its Applications in Communications, IWSDA'09

SP - 100

EP - 103

BT - Proceedings of the 4th International Workshop on Signal Design and Its Applications in Communications, IWSDA'09

T2 - 4th International Workshop on Signal Design and Its Applications in Communications, IWSDA'09

Y2 - 19 October 2009 through 23 October 2009

ER -