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|
#############################################################################
##
#A tblgener.gi GUAVA library Reinald Baart
#A Jasper Cramwinckel
#A Erik Roijackers
#A Eric Minkes
##
## Table generation
##
#H @(#)$Id: tblgener.gi,v 1.2 2003/02/12 03:49:21 gap Exp $
##
Revision.("guava/lib/tblgener_gi") :=
"@(#)$Id: tblgener.gi,v 1.2 2003/02/12 03:49:21 gap Exp $";
#############################################################################
##
#F CreateBoundsTable( <Sz>, <q> [, <info> ] ) . . constructs table of bounds
##
InstallMethod(CreateBoundsTable, "Sz, fieldsize, info", true,
[IsInt, IsInt, IsBool], 0,
function(Sz, q, info)
local RulesList, LBT, UBT, FillPoints, NumberUnchanged, RuleNumber, file,
WriteToFile, InitialTable, help, temp;
help :=
Concatenation("\n##\n",
"## Each entry [n][k] of one of the tables below contains\n",
"## a bound (the first table contains lowerbounds, the \n",
"## second upperbounds) for a code with wordlength n and \n",
"## dimension k. Each entry contains one of the following\n",
"## items: \n",
"## \n",
"## FOR LOWER- AND UPPERBOUNDSTABLE \n",
"## [ 0, <d>, <ref> ] from Brouwers table \n",
"## \n",
"## FOR LOWERBOUNDSTABLE \n",
"## empty k= 0, 1, n or d= 2 or (k= 2 and q= 2) \n",
"## 1 shortening a [ n + 1, k + 1 ] code \n",
"## 2 puncturing a [ n + 1, k ] code \n",
"## 3 extending a [ n - 1, k ] code \n",
"## [ 4, <dd> ] constr. B, of a [ n+dd, k+dd-1, d ] code\n",
"## [ 5, <k1> ] an UUV-construction with a [ n / 2, k1 ]\n",
"## and a [ n / 2, k - k1 ] code \n",
"## [ 6, <n1> ] concatenation of a [ n1, k ] and a \n",
"## [ n - n1, k ] code \n",
"## [ 7, <n1> ] taking the residue of a [ n1, k + 1 ] code\n",
"## \n",
"## FOR UPPERBOUNDSTABLE \n",
"## empty Griesmer bound \n",
"## 11 shortening a [ n + 1, k + 1 ] code \n",
"## 12 puncturing a [ n + 1, k ] code \n",
"## 13 extending a [ n - 1, k ] code \n",
"## [ 14, <dd> ] constr. B, with dd = dual distance \n");
InitialTable := function(to, lb)
local n, k, d, i, j, sum, BT;
BT := List([1..to], i-> [[i]]); #RepetitionCodes
for k in [2 .. to] do
BT[k][k] := [1]; #WholeSpaceCode
for n in [k+1 .. to] do
if lb then
BT[n][k] := [2];
else #upperbound
# Calculate Griesmer bound (for linear codes only)
# n >= Sum([0..k-1],i->DivUp(d,q^i));
d := BT[n-1][k][1] + 1;
sum := 0;
i := 1;
j := 1;
while j <= k do
# Calculate one term
sum := sum + QuoInt(d, i) + SignInt(d mod i);
i := i * q;
if i >= d then
# the rest will be one
sum := sum + k - j;
j := k;
fi;
j := j + 1;
od;
if sum <= n then
BT[n][k] := [d];
else
BT[n][k] := [d - 1];
fi;
fi;
od;
if q = 2 and k > 2 then #CordaroWagnerCode
BT[k][2] := [ 2*Int( (k+1) / 3 ) - Int(k mod 3 / 2 ) ];
fi;
od;
return BT;
end;
FillPoints := function( BT, lb )
local pt, initialfile;
GUAVA_TEMP_VAR := [false];
if lb then
initialfile := Filename(LOADED_PACKAGES.guava,
Concatenation("tbl/codes",
String(q),".g") );
else
initialfile := Filename(LOADED_PACKAGES.guava,
Concatenation("tbl/upperbd",
String(q),".g") );
fi;
if initialfile = fail then
Error("no table around for GF(",String(q),")");
fi;
if GUAVA_TEMP_VAR[1] = false then
GUAVA_TEMP_VAR := GUAVA_TEMP_VAR{[ 2 .. Length(GUAVA_TEMP_VAR) ]};
fi;
for pt in GUAVA_TEMP_VAR do
if (pt[1] <= Sz) and (pt[2] <= pt[1]) and
((lb and pt[3] > BT[pt[1]][pt[2]][1]) or
((not lb) and pt[3] < BT[pt[1]][pt[2]][1])) then
BT[pt[1]][pt[2]] := [pt[3], [ 0, pt[3], pt[4] ] ];
fi;
od;
return BT;
end;
WriteToFile := function(BT)
local list, k, n;
Print(Concatenation( "][", String(q), "] := [\n#V n = 1\n[ ]" ) );
for n in [2 .. Sz] do
list := [];
for k in [1 .. n] do
if Length( BT[n][k] ) = 2 then
list[k] := BT[n][k][2];
fi;
od;
Print(Concatenation(",\n#V n = ",String(n),"\n"), list);
od;
Print("];");
end;
#F begin of rules for lowerbound
RulesList := [];
# If a rule is added which is only valid for a special q (like q=2) the
# check for q should be around the Add(RulesList, function()....) :
# if q=2 then Add(RulesList, function() .... end); fi;
# Extending
Add(RulesList, function()
local n, k, number;
number := 0;
for n in [1..Sz-1] do
for k in [1..n] do
if q=2 and IsOddInt(LBT[n][k][1]) then
if LBT[n+1][k][1] < LBT[n][k][1] + 1 then
LBT[n+1][k] := [LBT[n][k][1] + 1, 3 ];
number := number + 1;
fi;
else
if LBT[n+1][k][1] < LBT[n][k][1] then
LBT[n+1][k] := [LBT[n][k][1], 3 ];
number := number + 1;
fi;
fi;
od;
od;
if info then Print(number," changes with Extending\n" ); fi;
return number > 0;
end);
# UUV Construction
Add(RulesList, function()
local n, k1, k2, d, d1, number;
number := 0;
for n in [ 3 .. Int( Sz / 2 ) ] do
for k1 in [ 1 .. n-2 ] do # V is a ( n, k1, d1 )-code
d1 := LBT[n][k1][1];
for k2 in [ k1+1 .. n-1 ] do # U is a ( n, k2, d2 )-code
d := 2 * LBT[n][k2][1];
if d1 < d then d := d1; fi; #faster then Minimum();
if LBT[2 * n][k1 + k2][1] < d then
LBT[2 * n][k1 + k2] := [d, [5, k2] ];
number := number + 1;
fi;
od;
od;
od;
if info then Print(number," changes with UUV\n" ); fi;
return (number > 0);
end);
# Concatenation
Add(RulesList, function()
local n1, n2, k, d, number;
number := 0;
for k in [ 2 .. Sz ] do
for n1 in [ k .. Int( Sz / 2 ) ] do
for n2 in [ n1 .. Sz - n1 ] do
d := LBT[n1][k][1] + LBT[n2][k][1];
if LBT[n1 + n2][k][1] < d then
LBT[n1 + n2][k] := [d, [6, n1 ] ];
number := number + 1;
fi;
od;
od;
od;
if info then Print(number," changes with Concatenation\n" ); fi;
return number > 0;
end);
# Puncturing
Add( RulesList,
function()
local n, k, number;
number := 0;
for n in Reversed([2..Sz]) do
for k in [1..n-1] do
if LBT[n-1][k][1] < LBT[n][k][1] - 1 then
LBT[n-1][k] := [LBT[n][k][1] - 1, 2 ];
number := number + 1;
fi;
od;
od;
if info then Print(number," changes with Puncturing\n" ); fi;
return (number > 0);
end);
# Shortening
Add(RulesList,
function()
local n, k, number;
number := 0;
for n in Reversed([5 .. Sz]) do
for k in [3 .. n-2] do
if LBT[n-1][k-1][1] < LBT[n][k][1] then
LBT[n-1][k-1] := [LBT[n][k][1], 1 ];
number := number + 1;
fi;
od;
od;
if info then Print(number," changes with Shortening\n" ); fi;
return (number > 0);
end);
# Taking the residue
Add(RulesList, function()
local n, k, temp, d, dnew, number;
number := 0;
for n in Reversed([ 4 .. Sz ]) do
temp := LBT[n];
for k in [ 3 .. n - 1 ] do
d := temp[k][1];
dnew := QuoInt(d,q)+SignInt(d mod q);# = (d/q) rounded up
if ( n - d > k ) and (LBT[ n - d ][ k - 1 ][1] < dnew) then
LBT[ n - d ][ k - 1 ] := [ dnew, [ 7, n ] ];
number := number + 1;
fi;
od;
od;
if info then Print(number," changes with Residue\n" ); fi;
return number > 0;
end);
# Construction B: M&S, Ch. 18, P. 9, Pg. 592
Add(RulesList, function()
local n, k, dd, number;
number := 0;
for n in Reversed([2..Sz]) do
for k in Reversed([1..n-1]) do
dd := UBT[n][n-k][1]; # upper bound for dual distance
if n-dd > 0 and k-dd+1 > 0 and
LBT[n-dd][k-dd+1][1] < LBT[n][k][1] then
LBT[n-dd][k-dd+1] := [ LBT[n][k][1], [4, dd] ];
number := number + 1;
fi;
od;
od;
if info then Print(number," changes with Construction B\n" ); fi;
return number > 0;
end);
#F begin of rules for lowerbound (not working)
# # ConversionFieldCode (it appears that this rule is not needed)
# if q = 2 then
# temp := BT4[1];
# Add(RulesList,
# function()
# local n, k, d, number;
# number := 0;
# for n in [ 2 .. Int(Sz/2) ] do
# for k in [ 1 .. n - 1 ] do
# d := temp[n][k][1];
# if LBT[2*n][2*k][1] < d then
# LBT[2*n][2*k] := [ d , 8 ];
# number := number + 1;
# fi;
# od;
# od;
# if info then Print(number," changes with ConversionField\n" ); fi;
# return number > 0;
# end);
# fi;
#F begin of rules for upperbound
# Shortening
Add(RulesList, function()
local n, k, number;
number := 0;
for n in [ 2 .. Sz-1 ] do
for k in [ 1 .. n - 1 ] do
if UBT[ n + 1 ][ k + 1 ][ 1 ] > UBT[ n ][ k ][ 1 ] then
UBT[ n + 1 ][ k + 1 ] := [ UBT[ n ][ k ][ 1 ], 11 ];
number := number + 1;
fi;
od;
od;
if info then Print(number," changes with Shortening\n" ); fi;
return number > 0;
end);
# Construction B
Add(RulesList, function()
local n, k, dd, s, number;
number := 0;
for n in [2..Sz] do
for k in [1..n-1] do
for s in [1..Sz-n-1] do
if s >= UBT[n+s][n-k+1][1] and
UBT[n+s][k+s-1][1] > UBT[n][k][1] then
UBT[n+s][k+s-1] := [ UBT[n][k][1], [14, s] ];
number := number + 1;
fi;
od;
od;
od;
if info then Print(number," changes with Construction B\n" ); fi;
return number > 0;
end);
# Extending
Add(RulesList, function()
local n, k, number;
number := 0;
for n in Reversed([2..Sz]) do
for k in [1..n-2] do
if q=2 and IsOddInt(UBT[n][k][1]) then
if UBT[n-1][k][1] > UBT[n][k][1]-1 then
UBT[n-1][k] := [ UBT[n][k][1]-1, 13 ];
number := number + 1;
fi;
else
if UBT[n-1][k][1] > UBT[n][k][1] then
UBT[n-1][k] := [ UBT[n][k][1], 13 ];
number := number + 1;
fi;
fi;
od;
od;
if info then Print(number," changes with Extending\n" ); fi;
return number > 0;
end);
# Puncturing
Add(RulesList, function()
local n, k, number;
number := 0;
for n in [ 2 .. Sz-1 ] do
for k in [ 2 .. n - 1 ] do
if UBT[ n + 1 ][ k ][ 1 ] > UBT[ n ][ k ][ 1 ] + 1 then
UBT[ n + 1 ][ k ] := [ UBT[ n ][ k ][ 1 ] + 1, 12 ];
number := number + 1;
fi;
od;
od;
if info then Print(number," changes with Puncturing\n" ); fi;
return number > 0;
end);
#F begin of rules for upperbound (not working)
#
# # Taking the residue
# Add(RulesList, function()
# local n, k;
# for n in [ 2 .. Sz-1 ] do
# for k in [ 2 .. n - 1 ] do
# if UBT[ n + q * UBT[ n ][ k ][ 1 ] ][ k + 1 ] >
# UBT[ n ][ k ][ 1 ] * q then
# UBT[ n + q * UBT[ n ] [ k ][ 1 ] ][ k + 1 ] :=
# [UBT[ n ][ k ][ 1 ] * q, [7, n + q * UBT[n][k][1]]];
# number := number + 1;
# fi;
# od;
# od;
# end);
#F begin of body
LBT := InitialTable( Sz, true );
LBT := FillPoints ( LBT, true );
UBT := InitialTable( Sz, false );
UBT := FillPoints ( UBT, false );
NumberUnchanged := 0;
RuleNumber := 1;
repeat
if RulesList[RuleNumber]() then
NumberUnchanged := 0;
else
NumberUnchanged := NumberUnchanged + 1;
fi;
if RuleNumber = Length(RulesList) then
RuleNumber := 1;
if info then Print("\n"); fi;
else
RuleNumber := RuleNumber + 1;
fi;
until NumberUnchanged >= Length(RulesList);
# This way of saving the tables to a file make use of a nasty trick,
# used to speed up things heavily
##LR - This trick is not yet working in GAP4. Until it does,
## the tables will not be printed to the file.
if info then Print("\nSaving the bound tables...\n"); fi;
file := Filename(LOADED_PACKAGES.guava,
Concatenation("tbl/bdtable",String(q),".g") );
PrintTo(file, "#A BOUNDS FOR q = ", String(q), help,
"\n\nGUAVA_BOUNDS_TABLE[1", WriteToFile(LBT),
"\n\nGUAVA_BOUNDS_TABLE[2", WriteToFile(UBT) );
return [LBT,UBT]; #just used for testing the program
end);
InstallOtherMethod(CreateBoundsTable, "Sz, fieldsize", true,
[IsInt, IsInt], 0,
function(Sz, q)
return CreateBoundsTable(Sz, q, false);
end);
InstallOtherMethod(CreateBoundsTable, "Sz, field, info", true,
[IsInt, IsField, IsBool], 0,
function(Sz, F, info)
return CreateBoundsTable(Sz, Size(F), info);
end);
InstallOtherMethod(CreateBoundsTable, "Sz, field", true,
[IsInt, IsField], 0,
function(Sz, F)
return CreateBoundsTable(Sz, Size(F), false);
end);
|
