It has only one row, corresponding to the coset of itself.

For contradiction sake, assume that and are in the same coset.

For small groups it is sometimes possible to perform a coset enumeration by hand.

This vector becomes the coset leader for the second row.

Then, is a valid codeword (since both terms are in the same coset).

We could, however, have chosen it as the first coset leader and constructed a different standard array.

For binary linear codes, they belong to the same coset.

For each coset leader u we calculate the syndrome uH'.

Following step 3, we complete the row by adding the coset leader to each codeword.

Physical states are in representations of the coset .

In other words, the indirect isometries form a single coset of E(n).

The elements in each cycle form a left coset of the subgroup generated by the element.

Choosing a constant is the same as choosing an element of the coset.

Modulo a prime, there is only the subgroup of squares and a single coset.

Fill out the row by adding the coset leader to the codeword at the top of each column.

If it is not, then a unique coset bijection exists such that .

The corresponding coset leader is the most likely error pattern and we assume that v+u was the codeword sent.

The coset table is used to store the relationships between the known cosets when multiplying by a generator.

We can fill in the entries of the coset table corresponding to the equations and .

Frequently D is required to be a complete set of coset representatives with some repetitions, but the repeated part has measure zero.

Thus a homogeneous space can be thought of as a coset space without a choice of origin.

There is no canonical preimage for a given function, but the set of all such preimages forms a coset.

What is more, the partial order induces a coset bijection defined by:

When H is maximal, the coset representation is primitive.

It's straightforward to show that, though the individual h depends on the choice of coset representatives, the value of the transfer does not.