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On the ReedMuller Codes
 Discrete Math
, 1992
"... We give a brief but complete account of all the essential facts concerning the ReedMuller and punctured ReedMuller codes. The treatment is new and includes an easy, direct proof of the fact that the punctured ReedMuller codes are the codes of the projective geometries over the binary field. We ..."
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We give a brief but complete account of all the essential facts concerning the ReedMuller and punctured ReedMuller codes. The treatment is new and includes an easy, direct proof of the fact that the punctured ReedMuller codes are the codes of the projective geometries over the binary field. We
Quantum ReedMuller codes
 IEEE Trans. Inf. Theory
"... A set of quantum error correcting codes based on classical ReedMuller codes is described. The codes have parameters [[n,k,d]] = [[2 r, 2 r − C(r,t) − 2 ∑ t−1 i=0 C(r,i), 2t + 2 t−1]]. The study of quantum information is currently stimulating much interest. Most of the basic concepts of classical i ..."
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A set of quantum error correcting codes based on classical ReedMuller codes is described. The codes have parameters [[n,k,d]] = [[2 r, 2 r − C(r,t) − 2 ∑ t−1 i=0 C(r,i), 2t + 2 t−1]]. The study of quantum information is currently stimulating much interest. Most of the basic concepts of classical
On Berman's characterization of the ReedMuller codes
 Part I, J. Statist. Plann. Inference
, 1996
"... In a seminal paper, [3], Berman studied codes as ideals in a modular group algebra. In particular, he showed that the ReedMuller codes could be characterized as the powers of the radical in the group algebra, over F 2, of an ..."
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In a seminal paper, [3], Berman studied codes as ideals in a modular group algebra. In particular, he showed that the ReedMuller codes could be characterized as the powers of the radical in the group algebra, over F 2, of an
Grassmannian packings from operator ReedMuller codes
 IEEE Trans. Info. Theory
"... Abstract—This paper introduces multidimensional generalizations of binary Reed–Muller codes where the codewords are projection operators, and the corresponding subspaces are widely separated with respect to the chordal distance on Grassmannian space. Parameters of these Grassmannian packings are de ..."
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Abstract—This paper introduces multidimensional generalizations of binary Reed–Muller codes where the codewords are projection operators, and the corresponding subspaces are widely separated with respect to the chordal distance on Grassmannian space. Parameters of these Grassmannian packings
Fast Generation and Covering Radius of ReedMuller Codes
, 2009
"... Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instruction, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments ..."
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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instruction, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments
PONS, REEDMULLER CODES, AND GROUP ALGEBRAS
"... Abstract In this work we develop the family of Prometheus orthonormal sets (PONS) in the framework of certain abelian group algebras. Classical PONS, considered in 1991 by J. S. Byrnes, turned out to be a rediscovery of the 1960 construction by G. R. Welti [28], and of subsequent rediscoveries by o ..."
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Abstract In this work we develop the family of Prometheus orthonormal sets (PONS) in the framework of certain abelian group algebras. Classical PONS, considered in 1991 by J. S. Byrnes, turned out to be a rediscovery of the 1960 construction by G. R. Welti [28], and of subsequent rediscoveries by other authors as well. This construction highlights the fundamental role played by group characters in the theory of PONS. In particular, we will relate classical PONS to idempotent systems in group algebras and show that signal expansions over classical PONS correspond to multiplications in the group algebra. The concept of a splitting sequence is critical to the construction of general PONS. We will characterize and derive closed form expressions for the collection of splitting sequences in terms of group algebra operations and group characters. The group algebras in this work are taken over direct products of the cyclic group of order 2. PONS leads to idempotent systems and ideal decompositions of these group algebras. The relationship between these special systems and ideal decompositions, and the analytic properties of PONS, is an open research topic. A second open research topic is the extension of this theory to group algebras over cyclic groups of order greater than 2.
L ReedMuller, NordstromRobinson, or Hamming
"... AbstractLet 8 be a code of length n over a field F, with automorphism group G; 8, denotes the subset of codewords of weight w. Our goal is to classify the vectors of IF " into orbits under G and to determine their distances from the various subcodes 8,. We do this for the firstorder ReedMull ..."
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AbstractLet 8 be a code of length n over a field F, with automorphism group G; 8, denotes the subset of codewords of weight w. Our goal is to classify the vectors of IF " into orbits under G and to determine their distances from the various subcodes 8,. We do this for the firstorder ReedMuller
Image Compression Based On ReedMuller Transforms
 In: Proc. Int. Conf. on Computational Intelligence and Multimedia Applications
, 1998
"... Wavelet Methods are revolutionizing the area of image processing and particularly compression. Haar transform is the simplest wavelet. Binary and multiplevalued nonsingular (NS) transforms [1] have similar local properties but use only logical operations and do not require additions and subtractions ..."
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and subtractions of Haar. It is then interesting to investigate the applications of NS transforms in these areas. The simplest of NS transforms is the Positive Polarity ReedMuller Transform, which was first used by Reddy and Pai [2] for image data compression. In this paper an attempt will be made to improve
Results 1  10
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218,582