http://web.eecs.utk.edu/~plank/plank/papers/CS-07-593/
And if you want an excellent description of how Reed-Solomon coding is efficiently implemented in Linux, try this:
http://en.wikipedia.org/wiki/Shamirs_Secret_Sharing
It lets you divide a message into (say) three parts, where any two parts are necessary and sufficient to reconstruct the message. Or into seven parts, where you need all the parts to reconstruct the message. Or whatever. The wikipedia page gives a very readable basic introduction to how it works.
Edit: it seems I conflated two different constructions of a field of order 256. Apologies. It's been a few semesters since abstract algebra >.<
Do you mean the numbers mod 256 that are co-prime with 256 form a field? Even that doesn't work because 1+3=4, so it's not closed under addition.
So I'm not sure what you mean.
Added in edit ...
Given any positive number n, the numbers from 1 to n-1 that are co-prime to n form a group with multiplication as the group operation, but that's still not a field, so I'm still confused as to what you might mean.
From wikipedia: "The finite fields are classified by size; there is exactly one finite field up to isomorphism of size p^k for each prime p and positive integer k." -http://en.wikipedia.org/wiki/Finite_field
As has been pointed out, Z/256Z has zero-divisors, so it's not a field.
"Powers of primes are also fields" doesn't mean anything; integers are integers, not fields. "Powers of primes are orders of finite fields" is correct; so there is a field of order 256, but it's not Z/256Z. (Rather, you get it by finding a degree-8 irreducible polynomial over Z/2Z, and adjoining a root of it. In fact, the article gives the specific polynomial x^8 + x^4 + x^3 + x + 1.)
1. Z/pZ is a field if and only if p is prime.
2. for every p prime and n>=1 there exists a unique (up to isomorphism) field, called Galois field (see any book of algebra for the proof).
3. you can build a field of p^n elements for every p and n>1, using polynomials over Z/pZ mod an irreducible polynomial of degree n, e.g. (see link) you can build F_{2^8} as polynomials with coefficients in Z_2 (i.e. bits) mod x^8 + x^4 + x^3 + x + 1. If you chose another irreducible polynomial, e.g. x^8 + x^4 + x^3 + x^2 + 1, then you get another representation of a field of 256 elements, but "structurally" they are the same (this should "explain" the expression "up to isomorphism")
If you read the post you don't need the summary because you just read the post, which btw, ends with a summary.
If you didn't read the post yet and know nothing about the field, your summary won't teach them anything, and more importantly it won't tell them anything about the post. It won't tell them it's a great, catchy, read, it might only scare them away with hard, math stuff.
If you didn't read the post yet and know a lot about the field, your summary won't teach them anything because there's nothing to teach. All it can do is create a false impression about what the articles is about, but looking at your other posts in this thread I see this is your intention anyway.
OpenSSL is useless for learning the basis of crypto (and the post is not about crypto, but whatever) because you need to understand the algorithms and the math aspect of the problem before you can follow and understand any terse and abstract implementation, and OpenSSL is also bad because it sacrifices lisibility for performance.
