subroutine gf64_osd(s3,cw)
   use jt65_generator_matrix

   real s3(64,63),xtmp(64),sympow_sorted(64,63),sympow(64,63)
   integer ideinterleave_indices(63),indxs(64),isymval_sorted(64,63),isymval(64,63)
   integer cw(63)
   integer indx(63)
   integer gmrb(12,63)
   integer correct(63)
   integer correctr(63)
   integer correct_sorted(63)
   integer candidate(63)
   integer candidater(63)
   integer itmp(63)
   logical mask(63),first
   data correct/   &  ! K1ABC W9XYZ EN37
      41,  0, 54, 46, 55, 29, 57, 35, 35, 48, 48, 61,  &
      21, 58, 25, 10, 50, 43, 28, 37, 10,  2, 61, 55,  &
      25,  5,  5, 57, 28, 11, 32, 45, 16, 55, 31, 46,  &
      44, 55, 34, 38, 50, 62, 52, 58, 17, 62, 35, 34,  &
      28, 21, 15, 47, 33, 20, 15, 28, 58,  4, 58, 61,  &
      59, 42,  2/
   data first/.true./
   save first,correctr

   if(first) then
      correctr=correct(63:1:-1)
!  find indices of deinterleaved symbols
      do i=1,63
         ideinterleave_indices(i)=i
      enddo
      call interleave63(ideinterleave_indices,-1)
      first=.false.
   endif
!  Sort the spectral powers in decreasing order, remove gray code
   do i=1,63
     xtmp=s3(:,i)
     call indexx(xtmp,64,indxs)
     sympow_sorted(:,i)=xtmp(indxs(64:1:-1))
     indxs=indxs-1
     call graycode65(indxs,64,-1)
     isymval_sorted(:,i)=indxs(64:1:-1)
   enddo
!  Deinterleave symbol powers.
   do i=1,63
     isymval(:,i)=isymval_sorted(:,ideinterleave_indices(i))
     sympow(:,i)=sympow_sorted(:,ideinterleave_indices(i))
   enddo

!  Now sort along the symbol index, using the largest spectral power at each index
   xtmp(1:63)=sympow(1,1:63)
   call indexx(xtmp(1:63),63,indx)

!  Calculate some statistics
   nhard=count(isymval(1,:).ne.correctr)
   nerrtop4=count(isymval(1,indx(60:63)).ne.correctr(indx(60:63)))
   nerrmid4=count(isymval(1,indx(56:59)).ne.correctr(indx(56:59)))
   nerrbot4=count(isymval(1,indx(52:55)).ne.correctr(indx(52:55)))
   do i=1,12
      if(isymval(1,indx(64-i)).ne.correctr(indx(64-i))) then
         write(*,'(i2,1x,64l1)') i,isymval(:,indx(64-i)).eq.correctr(indx(64-i))
      endif
   enddo
   write(*,*) 'nerr, nerrtop4, nerrmid4, nerrbot4',nhard,nerrtop4,nerrmid4,nerrbot4

! The best 12 symbols will be used as the Most Reliable Basis
! Reorder the columns of the generator matrix in order of decreasing quality.
!   do i=1,63
!      indx=isymval(64,63+1-i)+1
!      gmrb(:,i)=g(:,indx(63+1-i))
!   enddo
! Put the generator matrix in standard form so that top 12 symbols are
! encoded systematically.
!   call gf64_standardize_genmat(gmrb)

! Add various error patterns to the 12 basis symbols and reencode each one
! to get a list of codewords. For now, just find the zero'th order codeword.
!   call gf64_encode(gmrb,isymval(64,indx(63:52:-1)),candidate)
! Undo the sorting to put the codeword symbols back into the "right" order.
!   candidater=candidate(63:1:-1)
!   candidate(indx)=candidater

!   nerr=count(correctr.ne.candidate)
!write(*,*) 'Number of differences between candidate and correct codeword: ',nerr
!   if( nerr .eq. 0 ) write(*,*) 'Successful decode'
   return
end subroutine gf64_osd

subroutine gf64_standardize_genmat(gmrb)
   use gf64math
   integer gmrb(12,63),temp(63),gkk,gjk,gkkinv
   do k=1,12
      gkk=gmrb(k,k) 
      if(gkk.eq.0) then ! zero pivot - swap with the first row with nonzero value
         do kk=k+1,12
            if(gmrb(kk,k).ne.0) then
               temp=gmrb(k,:)
               gmrb(k,:)=gmrb(kk,:)
               gmrb(kk,:)=temp
               gkk=gmrb(k,k)
               goto 20
            endif
         enddo 
      endif
20    gkkinv=gf64_inverse(gkk)
      do ic=1,63
         gmrb(k,ic)=gf64_product(gmrb(k,ic),gkkinv)
      enddo
      do j=1,12
         if(j.ne.k) then
            gjk=gmrb(j,k)
            do ic=1,63
               gmrb(j,ic)=gf64_sum(gmrb(j,ic),gf64_product(gmrb(k,ic),gjk))
            enddo
         endif
      enddo
   enddo

   return
end subroutine gf64_standardize_genmat

subroutine gf64_encode(gg,message,codeword)
!
! Encoder for a (63,12) Reed-Solomon code.
! The generator matrix is supplied in array gg.
!
   use gf64math
   integer message(12)      !Twelve 6-bit data symbols
   integer codeword(63)     !RS(63,12) codeword
   integer gg(12,63)

   codeword=0
   do j=1,12
      do i=1,63
         iprod=gf64_product(message(j),gg(j,i))
         codeword(i)=gf64_sum(codeword(i),iprod)
      enddo
   enddo

   return
end subroutine gf64_encode