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QuantumSavory / QuantumClifford.jl

Clifford circuits, graph states, and other quantum Stabilizer formalism tools.
MIT License
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Adding classical Convolutional code to the ECC module #256

Open Fe-r-oz opened 2 months ago

Fe-r-oz commented 2 months ago

Classical Convolutional Code

Fe-r-oz commented 2 months ago

Classical Convolutional codes are fully implemented using Nemo. I have followed the Field Theoretic Implementation that was described in a paper, so that way, they can be described via Abstract Algebra.

TODO: look for properties of the convolutional codes that can be tested via FieldPolynomialRings.

Fe-r-oz commented 2 months ago

TODO: I am exploring about Direct Summands and how to check whether a Free Module is a Direct Summand given the Finite Field.

Fe-r-oz commented 2 months ago

Progress Update:

I had correspondence with authors of the paper of the code itself. I read the book and there is no mention of "free modules" at all, but they defined the it in terms of modules.

They have provided a definition in terms of Number theory that differs from what is provided in the book so I have requested further details.