Search results

* [[syndrome]], [[syndrome decoding]]

...alpha$ as zeros, the zero set of the code. The polynomial $S ( z )$ is the syndrome polynomial whose $i$th coefficient $S_i \in \mathbf{F} _ { q }$, $i = 0 , \ ...gth of the shift register and the feedback multiplier taps to generate the syndrome sequence to that point and terminates when the whole sequence is generated.

...s containing the binary expansions of the numbers $1,\ldots,2^r-1$. The [[syndrome]] of a word with a single error thus spells out the number of the position ...rows of a parity check matrix. A word is a codeword if and only if it has syndrome zero.