BCH+Hashing

a fast incremental [|Hash function] to transform a board position into a number of a set length, quite similar to Zobrist Hashing. It was proposed by Tony Warnock and Burton Wendroff in 1988, relying on [|BCH codes] invented by Alexis Hocquenghem in 1959 , and independently by Raj Chandra Bose and Dwijendra Kumar Ray-Chaudhuri in 1960. They used a BCH signature length of 81 (or more) bits to protect 16 bits from the full position string of 749 (64*12 - 2*2*8 + 4 + 8 + 1) bits, which is sufficient to avoid collisions within an 8 ply search. They stored 63 bits of the BCH signature as "lock" inside the table, and used 18 (or more) lower bits as index. Rainer Feldmann elaborates on BCH codes inside his thesis as well, and refers Elwyn Berlekamp's //Algebraic Coding Theory//. || toc =Quotes=
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 * [[image:Metamorphosis_of_Narcissus.jpg link="http://en.wikipedia.org/wiki/Metamorphosis_of_Narcissus"]] ||~  || **BCH Hashing**,
 * Salvador Dalí - [|Metamorphosis of Narcissus], 1937 ||~  ||^   ||

Tony Warnock
on //Search Tables in Computer Chess// :

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Kathe and Dan Spracklen
excerpt from their //Oral History// :

=See also=
 * Hash Table
 * Zobrist Hashing

=Publications=
 * Alexis Hocquenghem (**1959**). //Codes correcteurs d'erreurs//. Chiffres, Paris 2, pp. 147–156 (French)
 * Raj Chandra Bose, Dwijendra Kumar Ray-Chaudhuri (**1960**). //On A Class of Error Correcting Binary Group Codes//. [|Information and Control] Vol. 3, No. 1, pp. 68–79, ISSN 0890-5401, [|pdf]
 * Elwyn Berlekamp (**1968**). //Algebraic Coding Theory//. New York: McGraw-Hill. Revised ed., Aegean Park Press, (**1984**), ISBN 0894120638. [|amazon]
 * Jessie MacWilliams, Neil Sloane (**1981**). //[|The Theory of Error-Correcting Codes]//. North-Holland Mathematical Library, [|amazon]
 * Tony Warnock, Burton Wendroff (**1988**). //Search Tables in Computer Chess//. ICCA Journal, Vol. 11, No. 1
 * Rainer Feldmann (**1993**). //Game Tree Search on Massively Parallel Systems//. Ph.D. Thesis, [|pdf]
 * Jean-Christophe Weill (**1995**). //Programmes d'Échecs de Championnat: Architecture Logicielle Synthèse de Fonctions d'Évaluations, Parallélisme de Recherche//. Ph.D. Thesis. Université Paris 8, Saint-Denis, [|zipped ps] (French)
 * J. P. Grossman, [|Levente Jakab] (**2004**). //[|Using the BCH construction to generate robust linear hash functions]//. [|Information Theory Workshop, 2004. IEEE]

=Postings=
 * [|Re: Hash tablesClash!!!-What happens next?] by Tony Warnock, rgcc, March 17, 1994
 * [|Re: Hash functions for use with a transition table] by Ronald de Man, rgcc, March 7, 1997
 * [|How gracefully do BCH codes degrade] by Eb Oesch, [|Science Forum, math], May 20, 2008
 * [|Re: Overlapped Zobrist keys array] by Rémi Coulom, CCC, October 06, 2009

=External Links= > [|GF(2) from Wikipedia] > media type="youtube" key="zqxOJptzkcQ" height="360" width="480"
 * [|BCH codes from Wikipedia]
 * [|Berlekamp–Massey algorithm from Wikipedia]
 * [|Berlekamp–Welch algorithm from Wikipedia]
 * [|Coding theory from Wikipedia]
 * [|Coding Theory] by [|Andrew Thangaraj], Department of Electronics & Communication Engineering, [|Indian Institute of Technology Madras], [|YouTube] Videos
 * [|Cyclic code from Wikipedia]
 * [|Error detection and correction from Wikipedia]
 * [|Finite field from Wikipedia]
 * [|Forward error correction from Wikipedia]
 * [|MinT - Cyclic Codes (BCH-Bound)]
 * [|Root of unity modulo n from Wikipedia]
 * Hux Flux - Calculus, [|Cryptic Crunch], [|YouTube] Video

=References= =What links here?= include page="BCH Hashing" component="backlinks" limit="40"
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