Generalization of the well-known Walsh-Hadamard Transform (WHT), namely center-weighted Hadamard Transform (CWHT) and Complex Reverse-Jacket Transform (CRJT) have been proposed and their fast implementation and simple index generation algorithms have recently been reported. These transforms are of size 2~r x 2~r for integral values of r, and defined in terms of binary radix representation of integers. In this paper, using appropriate mixed-radix representation of integers, we present a generalized called General Reverse Jacket Transform(GRJT) that unifies all the three classes of transforms, WHT, CWHT and CRJT, and also applicable for any even length vectors, that is of size 2rx2r. A subclass of GRJT which includes CRJT (but not CWHT) is applicable for finite fields and useful for constructing error control codes.
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机译：已经提出了对著名的沃尔什-哈达玛变换（WHT），即中心加权哈达玛变换（CWHT）和复数逆夹套变换（CRJT）的推广，并且最近已经报道了它们的快速实现和简单的索引生成算法。对于r的整数值，这些变换的大小为2〜r x 2〜r，并以整数的二进制基数表示形式定义。在本文中，我们使用适当的整数混合基数表示形式，提出了一种通用的通用逆向夹克变换（GRJT），该变换统一了WHT，CWHT和CRJT这三类变换，并且还适用于任何偶数长度的矢量，大小为2rx2r。包含CRJT（但不包括CWHT）的GRJT子类适用于有限域，并且对构造错误控制代码很有用。
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