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Given a set of codewords generating a code, give a generating matrix, encode three data vectors, and decode one codeword.

Given a set of codewords generating a code, write down a generator matrix, encode three data vectors, and decode one codeword.

Given a generating matrix for a binary linear code, construct a parity check matrix, list all the codewords, list all the words in a given coset, give coset leaders, calculate syndromes for each coset, correct a codeword with one error.

Given a matrix in the field $\mathbb{Z}_n$. By reducing it to row-echelon form (or otherwise), find a basis for the row space of the matrix, as a list of vectors.

Given a set of vectors, find a basis which generates their span as a subspace of $\mathbb{Z}_n$.

List all vectors in a spanning set.

(repeated 3 times)

Find upper and lower bounds on the number of codewords in three maximal codes given their codeword lengths and minimum distances.

Uses Hamming, Singleton and Gilbert-Varshamov bounds.

Compute the information rate and minimum distance of some binary codes.

Compute tables of Hamming distances in given codes, then determine which codes are equivalent.

Find all words with given Hamming distance from a given codeword.