Phased burst error-correcting array codes
نویسندگان
چکیده
= p2 < h, by the assumption j 2 (3 / 2) m-(3 / 2). If t > t o we simply add points with errorvalue zero to the previously stated construction. This concludes 0 We have used the Hermitian curve because the rational points on this are so easy to handle, but this is probably also the case for many other curves. For a code C * (j) from a Hermitian curve, we have however more information in the decoding situation than the syndromes S a b , a + b 5 j , and this can be used to get a minor improvement. This fact has no influence on the general results for the algorithm as previously described, but since the extra information is readily available in this specific situation we will make some comments about it. From the curve equation yr+'-2T-I = 0 follows, in general, that the proof of the theorem. s a b + r + l = S a + r b + Sa+' b. Therefore, when we are decoding a code C * (j) , we know the syndromes S a b , a + b 5 j and S o j + Using all these syndromes as input to the algorithm one can realize, either by theoretical arguments or by experiments in concrete situations, that an error pattern as the one in Theorem 1 will be correctly decoded. To construct examples where the algorithm breaks down also with this extended input, one must change things a little. We choose the error points in the same way as before, but such that the smallest degree h of an error locator satisfies h=P1 + p 2 , p2 = m-3-(j-2h)-1. Let us now imagine, that we run the algorithm with all syndromes Sa 6 , a+b 5 j + l , as input. Then, with notation as above, because of (3.11) the rank of the matrixE.3+1-h is smaller that t (cf. Lemma 3).
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عنوان ژورنال:
- IEEE Trans. Information Theory
دوره 39 شماره
صفحات -
تاریخ انتشار 1993