What types of basic variations of the Hamming code are there and what are their objectives? I was taught the following version:
$$ L = n + k $$ $$ n \geq \log_2M $$ $$ k \ge \log_2(n+k+1) $$
where $M$ - number of alphabet symbols, $L$ - length of a codeword, $n$ - number of information bits, $k$ - number of parity bits. How does such a variation change the analysis and the algorithms involved as compared to the canonical way of coding?
Edit summary:
- I switched the notation to the one I was provided with originally.
- I switched the logarithm base from implicit $a$ to explicit 2.