I'm having trouble with a definition in the HQC Specification. From page 25f., in section 2.5.5.:
What does it mean to duplicate a code? Is it repeating each bit, similar to a repetition code?
Further, I don't understand the type of the function $F$: $\mathbb{F}_2^7 \to 3, 1, -1, -3^7$. Is this a typo, and it should map to $\{3, 1, -1, -3\}^7$ instead?
What do they mean by
where we started with transforming each block of three bits $x_1 x_2 x_3$ of the received vector in $(-1)^{x_1} + (-1)^{x_3} + (-1)^{x_3}$
?
Assuming this is the definition of $F$, I don't understand why $F$ takes 7 bits as input, instead of 3.
Should $F$ have the type $\mathbb{F}_2^3 \to \{3, 1, -1, -3\}$ instead? (Note the removed $\cdot^7$ and changed input space)
In section 2.5.7. they go through an example with multiplicity of 2 (instead of 3 like above):
Is this code equivalent to the concatenation of a repetition code and a Reed-Muller code? (where concatenation is what they define in def. 2.5.1.)
Thanks a lot in advance!
