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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)
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)
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)