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#############################################################################
##
#A codeman.gd GUAVA library Reinald Baart
#A &Jasper Cramwinckel
#A &Erik Roijackers
##
## This file contains functions for manipulating codes
##
#############################################################################
##
#F DualCode( <C> ) . . . . . . . . . . . . . . . . . . . . dual code of <C>
##
DeclareOperation("DualCode", [IsCode]);
#############################################################################
##
#F AugmentedCode( <C> [, <L>] ) . . . add words to generator matrix of <C>
##
DeclareOperation("AugmentedCode", [IsCode, IsObject]);
#############################################################################
##
#F EvenWeightSubcode( <C> ) . . . code of all even-weight codewords of <C>
##
DeclareOperation("EvenWeightSubcode", [IsCode]);
#############################################################################
##
#F ConstantWeightSubcode( <C> [, <w>] ) . all words of <C> with weight <w>
##
DeclareOperation("ConstantWeightSubcode", [IsCode, IsInt]);
#############################################################################
##
#F ExtendedCode( <C> [, <i>] ) . . . . . code with added parity check symbol
##
DeclareOperation("ExtendedCode", [IsCode, IsInt]);
#############################################################################
##
#F ShortenedCode( <C> [, <L>] ) . . . . . . . . . . . . . . shortened code
##
DeclareOperation("ShortenedCode", [IsCode, IsList]);
#############################################################################
##
#F PuncturedCode( <C> [, <list>] ) . . . . . . . . . . . . . punctured code
##
## PuncturedCode(C [, remlist]) punctures a code by leaving out the
## coordinates given in list remlist. If remlist is omitted, then
## the last coordinate will be removed.
##
DeclareOperation("PuncturedCode", [IsCode, IsList]);
#############################################################################
##
#F ExpurgatedCode( <C>, <L> ) . . . . . removes codewords in <L> from code
##
## The usual way of expurgating a code is removing all words of odd weight.
##
DeclareOperation("ExpurgatedCode", [IsCode, IsList]);
#############################################################################
##
#F AddedElementsCode( <C>, <L> ) . . . . . . . . . . adds words in list <L>
##
DeclareOperation("AddedElementsCode", [IsCode, IsList]);
#############################################################################
##
#F RemovedElementsCode( <C>, <L> ) . . . . . . . . removes words in list <L>
##
DeclareOperation("RemovedElementsCode", [IsCode, IsList]);
#############################################################################
##
#F LengthenedCode( <C> [, <i>] ) . . . . . . . . . . . . . . lengthens code
##
DeclareOperation("LengthenedCode", [IsCode, IsInt]);
#############################################################################
##
#F ResidueCode( <C> [, <w>] ) . . takes residue of <C> with respect to <w>
##
## If w is omitted, a word from C of minimal weight is used
##
DeclareOperation("ResidueCode", [IsCode, IsCodeword]);
#############################################################################
##
#F ConstructionBCode( <C> ) . . . . . . . . . . . code from construction B
##
## Construction B (See M&S, Ch. 18, P. 9) assumes that the check matrix has
## a first row of weight d' (the dual distance of C). The new code has a
## check matrix equal to this matrix, but with columns removed where the
## first row is 1.
##
DeclareOperation("ConstructionBCode", [IsCode]);
#############################################################################
##
#F ConstructionB2Code( <C> ) . . . . . . . . . . code from construction B2
##
## Construction B2 is mixtures of shortening and puncturing. Given an
## [n,k,d] code which has dual code of minimum distance s, we obtain
## an [n-s, k-s+2j+1, d-2j] code for each j with 2j+1 < s.
##
## For more details, see A. Brouwer (1998), "Bounds on the size of linear
## codes,", in Handbook of Coding Theory, V. S. Pless and W. C. Huffmann
## ed., pp. 311
##
## added by CJ, April 2006
##
DeclareOperation("ConstructionB2Code", [IsCode]);
#############################################################################
##
#F SubCode( <C>, [ <s> ] ) . . . . . . . . . . . . . . . . . . subcode of C
##
## Given C, an [n,k,d] code, return a subcode of C with dimension k-s.
## If s is not given, it is assumed 1.
##
## added by CJ, April 2006
DeclareOperation("SubCode", [IsCode, IsInt]);
#############################################################################
##
#F PermutedCode( <C>, <P> ) . . . . . . . permutes coordinates of codewords
##
DeclareOperation("PermutedCode", [IsCode, IsPerm]);
#############################################################################
##
#F StandardFormCode( <C> ) . . . . . . . . . . . . standard form of code <C>
##
DeclareOperation("StandardFormCode", [IsCode]);
#############################################################################
##
#F ConversionFieldCode( <C> ) . . . . . converts code from GF(q^m) to GF(q)
##
DeclareOperation("ConversionFieldCode", [IsCode]);
#############################################################################
##
#F CosetCode( <C>, <f> ) . . . . . . . . . . . . . . . . . . . coset of <C>
##
DeclareOperation("CosetCode", [IsCode, IsCodeword]);
#############################################################################
##
#F DirectSumCode( <C1>, <C2> ) . . . . . . . . . . . . . . . . . direct sum
##
## DirectSumCode(C1, C2) creates a (n1 + n2 , M1 M2 , min{d1 , d2} ) code
## by adding each codeword of the second code to all the codewords of the
## first code.
##
DeclareOperation("DirectSumCode", [IsCode, IsCode]);
#############################################################################
##
#F ConcatenationCode( <C1>, <C2> ) . . . . . concatenation of <C1> and <C2>
##
DeclareOperation("ConcatenationCode", [IsCode, IsCode]);
#############################################################################
##
#F DirectProductCode( <C1>, <C2> ) . . . . . . . . . . . . . direct product
##
## DirectProductCode constructs a new code from the direct product of two
## codes by taking the Kronecker product of the two generator matrices
##
DeclareOperation("DirectProductCode", [IsCode, IsCode]);
#############################################################################
##
#F UUVCode( <C1>, <C2> ) . . . . . . . . . . . . . . . u | u+v construction
##
## Uuvcode(C1, C2) # creates a ( 2n , M1 M2 , d = min{2 d1 , d2} ) code
## with codewords (u | u + v) for all u in C1 and v in C2
##
DeclareOperation("UUVCode", [IsCode, IsCode]);
#############################################################################
##
#F UnionCode( <C1>, <C2> ) . . . . . . . . . . . . . union of <C1> and <C2>
##
DeclareOperation("UnionCode", [IsCode, IsCode]);
#############################################################################
##
#F IntersectionCode( <C1>, <C2> ) . . . . . . intersection of <C1> and <C2>
##
DeclareOperation("IntersectionCode", [IsCode, IsCode]);
#############################################################################
##
#F ConstructionXCode( <C>, <A> ) ... code from Construction X
##
##
DeclareOperation("ConstructionXCode", [IsList, IsList]);
#############################################################################
##
#F ConstructionXXCode( <C1>, <C2>, <C3>, <A1>, <A2> ) ... code from Construction XX
##
##
DeclareOperation("ConstructionXXCode", [IsCode, IsCode, IsCode, IsCode, IsCode]);
#########################################################################
##
#F BZCode( <O>, <I> ) . . . . . . . . . . Blokh Zyablov concatenated code
##
## Given a set of outer codes O_i=[N, K_i, D_i] over GF(q^e_i), where
## i=1,2,...,t and a set of inner codes I_i=[n, k_i, d_i] over GF(q),
## BZCode returns a multilevel concatenated code with parameter
## [ n*N, e_1*K_1 + e_2*K_2 + ... + e_t*K_t, min(d_i * D_i)] over GF(q).
##
## Note that the set inner codes must satisfy chain condition, i.e.
## I_1=[n,k_1,d_1] < I_2=[n,k_2,d_2] < ... < I_t=[n,k_t,d_t] where
## 0=k_0 < k_1 < k_2 < ... < k_t.
##
## The dimensions of the inner code must satisfy the condition
## e_i = k_i - k_{i-1}, where GF(q^e_i) is the field of the ith
## outer code.
##
DeclareOperation("BZCode", [IsList, IsList]);
DeclareOperation("BZCodeNC", [IsList, IsList]);
#############################################################################
##
#F HullCode( <C> ) . . . . . . . . . . . . . . . . . . . . hull of <C>
##
DeclareOperation("HullCode", [IsCode]);
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