We introduce a family of binary array codes of size t/spl times, correcting multiple phased burst erasures of size t. The codes achieve maximal correcting capability, i.e., being considered as codes over GF(2/sup t/) they are MDS. The length of the codes is n=/spl Sigma//sub l=1//sup L/(/sub l//sup t/) where L is a constant or is slowly growing in t. The complexity of encoding and decoding is proportional to rnmL where r is the number of correctable erasures, and m is the smallest number such that 2/sup t/=1 modulo m. This compares favorably with the complexity of decoding codes obtained from the shortened general Reed-Solomon codes having the same parameters.
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机译：我们介绍了一系列大小为t / spl times / n的二进制数组代码，可校正大小为t的多相脉冲串擦除。该代码实现了最大的校正能力，即，被认为是GF（2 / sup t /）之上的代码，它们是MDS。代码的长度为n = / spl Sigma // sub l = 1 // sup L /（/ sub l // sup t /），其中L是常数或在t中缓慢增长。编码和解码的复杂度与rnmL成正比，其中r是可纠正的擦除次数，而m是最小的数目，以使得2 / sup t / = 1模为m。这与从具有相同参数的缩短的通用里德-所罗门码获得的解码码的复杂度相比具有优势。
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