This package is a part of Tongyuan's product. This repo is an archived version of it for the purpose of JuliaCN 2022 talk "Why I still recommend Julia -- composability and generic programming". This package provides a live example on how Julia beats MATLAB's C code by 1000x faster. The case is special, but the spirit that drives its design are common in Julia.

GaloisFieldNumbers.jl

This package provides a core integer type GF(aka GFNumber) to represent numbers in the galois field.

Construction

The main constructor is GF{M}, where M represents the number of bits(capacity). For instance, numbers in field GF{3} is between GF{3}(0) and GF{3}(2^3 - 1).

julia> typemin(GF{3}), typemax(GF{3})
(GF3(0), GF3(7))

julia> x = GF{3}(3) # is equivalent to GF3(3)
GF{3}(3)

julia> capacity(x), ppoly(x), eltype(x)
(3, GF3(11), UInt64)

The full constructor version is GF{M,P,T<:Unsigned}(x), where M represents the field capacity, P is the chosen prime polynomial for this galois field (default value is the smallest one), and T is the raw data type. These information can be extracted using capacity, ppoly and eltype, respectively.

For convenience, some alias are made for commonly used valid M value -- from GF1 to GF16. The difference between GF3 and GF{3} is that GF3 is a concrete type with P=11 and T=UInt, while GF{3} is a partially constructed type (neither concrete or abstract). For instance,

julia> x = GF3[1, 2, 3] # equivalent to GF{3,11,UInt}[1, 2, 3]
3-element Vector{GF3}:
 1
 2
 3

julia> x = GF{3}[1, 2, 3]
3-element Vector{GFNumber{3}}:
 GF3(1)
 GF3(2)
 GF3(3)