TABLE OF CONTENTS We can trap bursts with cyclic codes, but the Fire cyclic codes are particularly well adapted to this kind of decoding. H. Imai has generalized this technique to the case of Fire codes with two dimensions. We will, therefore, describe the trapping of bursts by means of a binary Fire code, of length n and generator g( X).
We will suppose that the burst b( X) has a maximum corrigible length b. The other cases are directly derive from here. It is thus represented as a polynomial of the b ? 1 degree, and with a constant 1.
The received word r( X) is equal to the transmitted word c( X), to which a burst X ib( X) has been added during transmission. Simultaneously with calculating the remainder of r( X) in an associated divisor register g( X), R g we memorize r( X) in a register with shifts, R of length n. We wish to achieve that the burst also be at the output of the register associated with g( X) when it is at the output of the register with shifts. By simple addition we then eliminate the burst. The two following propositions bring the solution.
