fix parity_matrix generation and parameter calculations in classical LiftedCode

[Fe-r-oz]

The classical LiftedProduct code parity checks matrices have not really been used as seed for any quantum code so this bug was not detected. Reference: #356

Edit:

🐞 Stacktrace of MethodError when calling parity_checks

ERROR: MethodError: no method matching lift(::typeof(representation_matrix), ::Matrix{GroupAlgebraElem{FqFieldElem, GroupAlgebra{…}}})
The function `lift` exists, but no method is defined for this combination of argument types.

Closest candidates are:
  lift(::fqPolyRepPolyRingElem, ::Any)
   @ Hecke ~/.julia/packages/Hecke/RwzTY/src/LocalField/Poly.jl:117
  lift(::ZZRing, ::zzModRingElem)
   @ Nemo ~/.julia/packages/Nemo/mOOnX/src/flint/nmod.jl:35
  lift(::ZZRing, ::ZZModRingElem)
   @ Nemo ~/.julia/packages/Nemo/mOOnX/src/flint/fmpz_mod.jl:35
  ...
Stacktrace:
 [1] parity_checks(c::QuantumCliffordHeckeExt.LiftedCode)
   @ QuantumCliffordHeckeExt ~/Desktop/QuantumClifford.jl/ext/QuantumCliffordHeckeExt/lifted.jl:107
 [2] parity_matrix(c::QuantumCliffordHeckeExt.LiftedCode)
   @ QuantumClifford.ECC ~/Desktop/QuantumClifford.jl/src/ecc/ECC.jl:148
 [3] top-level scope
   @ REPL[100]:1
Some type information was truncated. Use `show(err)` to see complete types.

Additionally, I have not added doctest for this first wrapper constructor that calls the second constructor and I am not sure if there is any potential bug calling this or not.

QuantumClifford.jl/ext/QuantumCliffordHeckeExt/lifted.jl

Line 68 in def729f

function LiftedCode(A::Matrix{GroupAlgebraElem{FqFieldElem, <: GroupAlgebra}}; GA::GroupAlgebra=parent(A[1,1]))

• The code is properly formatted and commented.
• Substantial new functionality is documented within the docs.
• All new functionality is tested.
• All of the automated tests on github pass.
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Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 85.16%. Comparing base (cd76712) to head (c8c7230).

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #525      +/-   ##
==========================================
+ Coverage   85.11%   85.16%   +0.05%     
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+ Misses       1079     1075       -4     

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[Fe-r-oz]

This PR is ready for review, Thank you!

[Krastanov]

thanks, this is great! Could you add a small test for what used to fail, just to make sure that similar failures do not get reintroduced at some point.

[Fe-r-oz]

Thank you for your feedback! I have added basic tests with tests_nowarn that just check there is no method error calling stuff that resulted in method errors, I will check literature about properties on these classical codes. I have placed the tests in test_ecc_throws.jl.

The stacktrace of the errors resulting from code_s, code_n and the suggested fix:

julia> import Hecke; import QuantumClifford.ECC: LiftedCode, code_n, code_k, code_s
julia> import QuantumClifford.ECC.QECCore: parity_matrix
julia>  base_matrix = [0 0 0 0; 0 1 2 5; 0 6 3 1]; l = 3;
julia> c LiftedCode(base_matrix, l);
julia> size(zero(c.GA), 2 or 1) # currently, we use this in code_n or code_s that throw error
ERROR: MethodError: no method matching size(::GroupAlgebraElem{FqFieldElem, GroupAlgebra{FqFieldElem, FinGenAbGroup, FinGenAbGroupElem}}, ::Int64)
The function `size` exists, but no method is defined for this combination of argument types.

Closest candidates are:
  size(::BitVector, ::Integer)
   @ Base bitarray.jl:107
  size(::Hecke.ZZRingElem_Array_Mod.ZZRingElem_Array, ::Int64)
   @ Hecke ~/.julia/packages/Hecke/RwzTY/src/Sparse/ZZRow.jl:65
  size(::Type{SIMD.Vec{N, T}}, ::Integer) where {N, T}
   @ SIMD ~/.julia/packages/SIMD/hyXY3/src/simdvec.jl:74
  ...

Stacktrace:
 [1] top-level scope
   @ REPL[30]:1

julia> size(c.repr(zero(c.GA)), 2)
3

julia> size(c.A, 2) * order(group(c.GA))
12
julia> size(c.A, 1) * order(group(c.GA)) 
9

julia> size(c.A, 2) * size(c.repr(zero(c.GA)), 2)
12
julia> size(c.A, 1) * size(c.repr(zero(c.GA)), 1)
9

Defined code_k for the classical code as $k = n - rank(H)$

[Fe-r-oz]

ping @Krastanov

[Fe-r-oz]

@Krastanov, when you have a moment, please let me know your feedback. I have fixed the LiftedCode constructor, added it to the CECC base, and completed the code review suggestions. Please let me know if it's ready to merge. The test failures are unrelated to this PR. Thank you!