Philippe Piret

Permutations preserving divisibility

We give a proof of a theorem on the common divisibility of polynomials and permuted polynomials (over GF(2)) by a polynomial g(x).

Bolt interleavers for turbo codes

A procedure is described to produce efficient turbo-code interleavers. It is well suited to the selection of interleavers that produce a large minimum distance for the resulting turbo codes. A feature of these interleavers is that the final state of the two elementary encoders is simultaneously zero. Examples are given and the corresponding codes are simulated. They seem to be among the best ones for rate 1/3 turbo codes.

Aggregate error locator and error value computation in AG codes

The aggregate error locator is defined and a computation method is given. The aggregate error locator is then used in a type of Forney algorithm to compute the error values in the received words of a Ca,b algebraic geometry code.

An encoder to match Reed-Solomon codes over GF(q) to a subalphabet of GF(q)

One describes procedures to generate the codewords of a Reed-Solomon code over GF(2/sup m/) having all their symbols in a GF(2) subspace of GF(2/sup m/). Some of the described encoders are systematic binary encoders and some are only partly systematic.