Changeset 76afcd in git for Singular/LIB/decodegb.lib


Ignore:
Timestamp:
Mar 25, 2009, 12:15:16 PM (15 years ago)
Author:
Stanislav Bulygin <bulygin@…>
Branches:
(u'spielwiese', 'fe61d9c35bf7c61f2b6cbf1b56e25e2f08d536cc')
Children:
087a94afc4dc0923c87d4d3d336e0ab8ae621a77
Parents:
fe919cbede83a96748fd037a48aa15876e31e41e
Message:
proof-reading is done


git-svn-id: file:///usr/local/Singular/svn/trunk@11588 2c84dea3-7e68-4137-9b89-c4e89433aadc
File:
1 edited

Legend:

Unmodified
Added
Removed

  • Singular/LIB/decodegb.lib

    rfe919c r76afcd  
    11///////////////////////////////////////////////////////////////////////////////
    2 version="$Id: decodegb.lib,v 1.9 2009-01-14 16:07:03 Singular Exp $";
     2version="$Id: decodegb.lib,v 1.10 2009-03-25 11:15:16 bulygin Exp $";
    33category="Coding theory";
    44info="
    … …  
    1212 is worked out here as well. We also (for comparison) enable to work with the
    1313 system of Fitzgerald-Lax. We provide some auxiliary functions for further
    14  manipulations and decoding. For an overview of the methods mentioned above @ref{Decoding codes with GB}
     14 manipulations and decoding. For an overview of the methods mentioned above @ref{Decoding codes with GB}.
    1515 For the vanishing ideal computation the algorithm of Farr and Gao is
    1616 implemented.
    … …  
    9090
    9191proc sysCRHT (int n, list defset, int e, int q, int m, list #)
    92 "USAGE:   sysCRHT(n,defset,e,q,m,[k]); n,e,q,m,k int, defset list of int's
     92"USAGE:   sysCRHT(n,defset,e,q,m,[k]); n,e,q,m,k are int, defset list of int's
    9393@format
    9494         - n length of the cyclic code,
    … …  
    281281
    282282proc sysNewton (int n, list defset, int t, int q, int m, list #)
    283 "USAGE:   sysNewton (n,defset,t,q,m,[tr]); n,t,q,m,tr int, defset list int's
     283"USAGE:   sysNewton (n,defset,t,q,m,[tr]); n,t,q,m,tr int, defset is list int's
    284284@format
    285285         - n is length,
    … …  
    296296         the corresponding ideal 'newton' with the generalized Newton
    297297         identities. With its help one can solve the decoding problem. For
    298          basics of the method @ref{Cooper philosophy}.
     298         basics of the method @ref{Generalized Newton identities}.
    299299SEE ALSO: sysCRHT, sysBin
    300300EXAMPLE:  example sysNewton; shows an example
    … …  
    471471@format
    472472          - v a number if errors,
    473           - Q is a generating set of the code,
     473          - Q is a defining set of the code,
    474474          - n the length,
    475475          - odd is an additional parameter: if
    476            set to 1, then the generating set is enlarged by odd elements,
    477            which are 2^(some power)*(some elment in the gen.set) mod n
     476           set to 1, then the defining set is enlarged by odd elements,
     477           which are 2^(some power)*(some elment in the def.set) mod n
    478478@end format
    479479RETURN:    the ring with the resulting system called 'bin'
    480480THEORY:  Based on Q of the given cyclic code, the procedure constructs
    481          the corresponding ideal 'bin' with the use of Waring function.
     481         the corresponding ideal 'bin' with the use of the Waring function.
    482482         With its help one can solve the decoding problem.
    483483         For basics of the method @ref{Generalized Newton identities}.
    … …  
    657657"USAGE:   sysQE(check,y,t,[fieldeq,formal]);check,y matrix;t,fieldeq,formal int
    658658@format
    659         - check is the check matrix of the code
     659        - check is a parity check matrix of the code
    660660        - y is a received word,
    661661        - t the number of errors to be corrected,
    … …  
    663663        - if formal=0, field equations on (known) syndrome variables
    664664          are not added, in order to add them (note that the exponent should
    665           be as a number of elements in the INITIAL alphabet) one
     665          be equal to the number of elements in the INITIAL alphabet) one
    666666          needs to set formal>0 for the exponent
    667667@end format
    … …  
    669669THEORY:  Based on 'check' of the given linear code, the procedure constructs
    670670         the corresponding ideal that gives an opportunity to compute
    671          unknown syndrome of the received word y. Further
    672          one is able to solve the decoding problem.
     671         unknown syndrome of the received word y. After computing the unknown
     672         syndromes one is able to solve the decoding problem.
    673673         For basics of the method @ref{Decoding method based on quadratic equations}.
    674674SEE ALSO: sysFL
    … …  
    860860
    861861proc errorInsert(matrix y, list pos, list val)
    862 "USAGE:  errorInsert(y,pos,val); y is matrix, pos,val list of int's
     862"USAGE:  errorInsert(y,pos,val); y is matrix, pos,val are list of int's
    863863@format
    864864        - y is a (code) word,
    … …  
    900900
    901901proc errorRand(matrix y, int num, int e)
    902 "USAGE:    errorRand(y, num, e); y matrix, num,e int
     902"USAGE:    errorRand(y, num, e); y is matrix, num,e are int
    903903@format
    904904          - y is a (code) word,
    … …  
    10141014        - a is a primitive element of the field.
    10151015@end format
    1016 NOTE:   An MDS matrix is constructed in the following way. We take a to be a
     1016NOTE:   An MDS matrix is constructed in the following way. We take 'a' to be a
    10171017        generator of the multiplicative group of the field. Then we construct
    1018         the Vandermonde matrix with this a.
     1018        the Vandermonde matrix with this 'a'.
    10191019ASSUME:   extension field should already be defined
    1020 RETURN:   a matrix with the MDS property
     1020RETURN:   a matrix with the MDS property. @xref{Decoding method based on quadratic equations}
     1021          for more info.
    10211022EXAMPLE:  example genMDSMat; shows an example
    10221023"
    … …  
    11381139          - t is an upper bound for the number of errors one wants to correct
    11391140@end format
     1141NOTE:     The method described in @ref{Decoding method based on quadratic equations}
     1142          is used for decoding.
    11401143ASSUME:   Errors in rec should be correctable, otherwise the output is
    11411144          unpredictable
    … …  
    13221325"USAGE:     decodeCode(check, ntrials, [e]); check matrix, ntrials,e int
    13231326@format
    1324            - check is a check matrix for the code,
     1327           - check is a parity check matrix for the code,
    13251328           - ntrials is the number of received vectors per code to be
    13261329           corrected.
    … …  
    17301733"USAGE:    sysFL (check,y,t,e,s); check,y matrix, t,e,s int
    17311734@format
    1732           - check is a check matrix of the code,
     1735          - check is a parity check matrix of the code,
    17331736          - y is a received word,
    17341737          - t the number of errors to correct,
    … …  
    19921995"USAGE:    decodeRandomFL(redun,p,e,n,t,ncodes,ntrials,minpol);
    19931996@format
    1994           - n is length of codes generated, redun = redundancy of codes
    1995           generated,
     1997          - n is length of codes generated,
     1998          - redun = redundancy of codes generated,
    19961999          - p is characteristics,
    19972000          - e is the extension degree,
Note: See TracChangeset for help on using the changeset viewer.