Algorithm for generating an error correction code of size k by n bits

Question

I want to generate n-bit code for k different inputs that I want to classify. The main requirement of this code is the error correction criterion: maximizing the minimum pairwise distance between any two encodings of different inputs. I do not need this to be precise - it will be approximate, and ease of use and speed of computational implementation is also a priority.

In the general case, n will be in hundreds, k in tens.

Also, is there a reasonable tight binding to the minimum hamming distance between k different n-bit binary encodings?

Answer 1

, . , , .

, n "k, , , k- n. ( k n .) , -, , , . , , .

-, n "k, BCH q = 2. , BCH.

n "k , . : t, ((t-1)/2). , , . , 2 ⁿ , ( ) . , . .