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Majority-logic decoding is attractive for three reasons: (I) It can be simply implemented; (2) the decoding delay is short; and (3) its performance, while suboptimal, is always superior to bounded distance decoding. For these reasons, majority-logic decodable cyclic codes are very suitable f o r error control in high speed digital data transmission systems.(More)
Today's most advanced scientific applications run on large clusters consisting of hundreds of thousands of processing cores, access state of the art parallel file systems that allow files to be distributed across hundreds of storage targets, and utilize advanced interconnections systems that allow for theoretical I/O bandwidth of hundreds of gigabytes per(More)
In this paper we consider the question of how much space is needed to represent a set. Given a finite universe U and some subset V (called the vocabulary), an <underline>exact membership tester</underline> is a procedure that for each element s in U determines if s is in V. An <underline>approximate membership tester</underline> is allowed to make mistakes:(More)
Various authors (especially Scott, Egli, and Constable) have introduced concepts of " basis " for various classes of partially ordered sets (posets). This paper studies a basis concept directly analogous to the concept of a basis for a vector space. The new basis concept includes that of Egli and Constable as a special case, and one of their theorems is a(More)