adding classical Reed-Muller Code

CHANGELOG.md

@@ -7,6 +7,7 @@
 
 ## v0.9.1 - 2024-03-20
 
+- Implementedd the classical Reed-Muller code 
 - Implemented `iscss` function to identify whether a given code is known to be a CSS (Calderbank-Shor-Steane) code.
 
 ## v0.9.0 - 2024-03-19

src/ecc/ECC.jl

@@ -17,6 +17,7 @@ export parity_checks, parity_checks_x, parity_checks_z, iscss,
     isdegenerate, faults_matrix,
     naive_syndrome_circuit, shor_syndrome_circuit, naive_encoding_circuit,
     RepCode,
+    ReedMuller,
     CSS,
     Shor9, Steane7, Cleve8, Perfect5, Bitflip3,
     Toric, Gottesman,
@@ -345,4 +346,5 @@ include("codes/shorcode.jl")
 include("codes/clevecode.jl")
 include("codes/toric.jl")
 include("codes/gottesman.jl")
+include("codes/reedmullercode.jl")
 end #module

src/ecc/codes/reedmullercode.jl

@@ -0,0 +1,31 @@
+abstract type ClassicalCode end
+
+struct ReedMuller <: ClassicalCode
+    r::Int
+    m::Int
+
+    function ReedMuller(r, m)
+        if r < 0 || m < 1
+            throw(ArgumentError("Invalid parameters: r must be non-negative and m must be positive"))
+        end
+        new(r, m)
+    end
+end
+
+function construct(m, i)
+    return repeat([fill(1, 2^(m - i - 1)); fill(0, 2^(m - i - 1))], outer = 2^i)
+end
+
+function vmult(vecs...)
+    return [reduce(*, a, init=1) for a in zip(vecs...)]
+end
+
+function parity_checks(c::ReedMuller)
+    r=c.r
+    m=c.m
+    rx = [construct(m, i) for i in 0:m - 1]
+    row_matrices = [reduce(vmult, [rx[i + 1] for i in S], init = ones(Int, 2^m)) for s in 0:r for S in combinations(0:m - 1, s)]
+    rows = length(row_matrices)
+    cols = length(row_matrices[1])
+    H = reshape(vcat(row_matrices...), cols, rows)'
+end

test/test_throws.jl

@@ -1,5 +1,6 @@
 using Test
 using QuantumClifford
+using QuantumClifford.ECC
 using QuantumClifford: rank, mul_left!, mul_right!
 using InteractiveUtils: subtypes
 
@@ -65,3 +66,6 @@ for m in [sMX,sMZ,sMY,sMRX,sMRZ,sMRY]
     @test_throws ArgumentError m(0,1)
     @test_throws ArgumentError m(-1,0)
 end
+
+@test_throws ArgumentError ReedMuller(-1, 3)
+@test_throws ArgumentError ReedMuller(1, 0)