# cosets

Produce cyclotomic cosets for Galois field

## Syntax

```cst = cosets(m) ```

## Description

`cst = cosets(m) ` produces cyclotomic cosets mod `2^m-1`. Each element of the cell array `cst` is a Galois array that represents one cyclotomic coset.

A cyclotomic coset is a set of elements that share the same minimal polynomial. Together, the cyclotomic cosets mod `2^m-1` form a partition of the group of nonzero elements of GF(`2^m`). For more details on cyclotomic cosets, see the works listed in References.

## Examples

The commands below find and display the cyclotomic cosets for GF(8). As an example of interpreting the results, `c{2}` indicates that A, A2, and A2 + A share the same minimal polynomial, where A is a primitive element for GF(8).

```c = cosets(3); c{1}' c{2}' c{3}'```

The output is below.

```ans = GF(2^3) array. Primitive polynomial = D^3+D+1 (11 decimal) Array elements = 1 ans = GF(2^3) array. Primitive polynomial = D^3+D+1 (11 decimal) Array elements = 2 4 6 ans = GF(2^3) array. Primitive polynomial = D^3+D+1 (11 decimal) Array elements = 3 5 7 ```

## References

[1] Blahut, Richard E., Theory and Practice of Error Control Codes, Reading, MA, Addison-Wesley, 1983, p. 105.

[2] Lin, Shu, and Daniel J. Costello, Jr., Error Control Coding: Fundamentals and Applications, Englewood Cliffs, NJ, Prentice-Hall, 1983.

## Version History

Introduced before R2006a