# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
A generalized reverse jacket transform. (English) Zbl 1014.65150

Summary: Generalizations of the well-known Walsh-Hadamard transform (WHT), namely the center-weighted Hadamard transform (CWHT) and the 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 ${2}^{r}×{2}^{r}$ for integral values or $r$, and defined in terms of the binary radix representation of integers.

In this paper, using an appropriate mixed-radix representation of integers, we present a generalized transform called the general reverse jacket transform (GRJT) that unifies all the three classes of transforms, WHT, CWHT, and CRJT, and that is also applicable for any even length vectors, that is of size $2r×2r$. A subclass of GRJT which includes CRJT (but not CWHT) is applicable for finite fields and useful for constructing error control codes.

##### MSC:
 65T50 Discrete and fast Fourier transforms (numerical methods) 94A08 Image processing (compression, reconstruction, etc.)