coset

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.