His primary areas of study are Discrete mathematics, Combinatorics, Linear code, Block code and Group code. His Discrete mathematics study combines topics from a wide range of disciplines, such as Ring and Dual code. His Combinatorics research is multidisciplinary, relying on both Lattice, Leech lattice and Laplace operator.
Patrick Solé focuses mostly in the field of Linear code, narrowing it down to topics relating to Hamming code and, in certain cases, Concatenated error correction code. His Block code study combines topics in areas such as Quantum computer, Hermitian matrix and Product. In his research, Quadratic residue, Quadratic residue code, Universal code and Enumerator polynomial is intimately related to Binary Golay code, which falls under the overarching field of Group code.
His main research concerns Combinatorics, Discrete mathematics, Linear code, Ring and Block code. His Combinatorics research includes themes of Cyclic code, Upper and lower bounds and Function. His Discrete mathematics research is multidisciplinary, incorporating elements of Binary code, Binary number and Hamming code, Group code.
His study in Concatenated error correction code extends to Linear code with its themes. His research investigates the link between Ring and topics such as Trace that cross with problems in Character. His Block code study focuses on Reed–Muller code in particular.
Patrick Solé mostly deals with Combinatorics, Discrete mathematics, Ring, Circulant matrix and Finite field. His Combinatorics study integrates concerns from other disciplines, such as Chain and Code. As a member of one scientific family, Patrick Solé mostly works in the field of Discrete mathematics, focusing on Generalization and, on occasion, Matrix.
The Ring study combines topics in areas such as Trace and Order. His studies deal with areas such as Polynomial and Secret sharing as well as Finite field. His work in Abelian group addresses subjects such as Gauss sum, which are connected to disciplines such as Linear code and Degree.
Combinatorics, Discrete mathematics, Ring, Primitive root modulo n and Finite field are his primary areas of study. His work on Degree as part of general Combinatorics study is frequently linked to Alphabet, bridging the gap between disciplines. In the field of Discrete mathematics, his study on Strongly regular graph overlaps with subjects such as Homogeneous.
His studies in Ring integrate themes in fields like Trace, Chain, Order, Metric and Abelian group. As part of one scientific family, Patrick Solé deals mainly with the area of Abelian group, narrowing it down to issues related to the Gauss sum, and often Lee distance, Linear code and Expander code. His biological study spans a wide range of topics, including Circulant matrix, Dual and Generator matrix.
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The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes
A.R. Hammons;P.V. Kumar;A.R. Calderbank;N.J.A. Sloane.
IEEE Transactions on Information Theory (1994)
Type II codes over F/sub 2/+uF/sub 2/
S.T. Dougherty;P. Gaborit;M. Harada;P. Sole.
IEEE Transactions on Information Theory (1999)
On the algebraic structure of quasi-cyclic codes .I. Finite fields
San Ling;P. Sole.
IEEE Transactions on Information Theory (2001)
Pyramidal lattice vector quantization for multiscale image coding
M. Barlaud;P. Sole;T. Gaidon;M. Antonini.
IEEE Transactions on Image Processing (1994)
Quaternary quadratic residue codes and unimodular lattices
A. Bonnecaze;P. Sole;A.R. Calderbank.
IEEE Transactions on Information Theory (1995)
Skew constacyclic codes over Galois rings
Delphine Boucher;Patrick Sole;Félix Ulmer.
Advances in Mathematics of Communications (2008)
Type II codes over Z/sub 4/
A. Bonnecaze;P. Sole;C. Bachoc;B. Mourrain.
international symposium on information theory (1997)
Vera Pless;Patrick Solé;Zhongqiang Qian.
Finite Fields and Their Applications (1997)
A linear construction for certain Kerdock and Preparata codes
A. R. Calderbank;A. R. Hammons;P. Vijay Kumar;N. J. A. Sloane.
Bulletin of the American Mathematical Society (1993)
A quaternary cyclic code, and a family of quadriphase sequences with low correlation properties
Proceedings of the third international colloquium on Coding theory and applications (1989)
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