I've been studying Hamming codes, specifically in their use in LoRa - the spread spectrum modulation scheme. The specs for LoRa mention four, selectable forward error correcting constructs: 4/5, 4/6, 4/7 and 4/8. Outside LoRa it seems they'd be referred to as [5,4], [6,4] etc.
I think I understand the [7,4] variety (which appears to be the most common, at least among academic discussion of Hamming), as well as the [8,4] - which seems to be the adding of one overall parity bit to the [7,4] version.
But the [5,4] and [6,4] I have not been able to find any info on. Can someone explain?
$[5,4]$ and $[6,4]$ are non-correcting. They can still be used for error detection ($[6,4]$ having greater certainty than $[5,4]$) and play a role in elimination of strings of all-zeros or all-ones bit that can occur in the uncoded input data.