منابع مشابه
Decimal Codes
To make error correcting codes easier to use and analyze, it is necessary to impose some algebraic structure on them. It is especially useful to have an alphabet in which it is possible to add, subtract, multiply and divide without restriction. In other words we wish to construct a finite field. Evarist Galois (1811-32), a French mathematician who died in a duel at the age of 20 introduced fini...
متن کاملNote on Perfect Forests
A spanning subgraph F of a graph G is called perfect if F is a forest, the degree dF (x) of each vertex x in F is odd, and each tree of F is an induced subgraph of G. We provide a short proof of the following theorem of A.D. Scott (Graphs & Combin., 2001): a connected graph G contains a perfect forest if and only if G has an even number of vertices.
متن کاملA note on perfect dissections of an equilateral triangle
A perfect dissection of a polygon P into a polygon P ′ is a decomposition of P into internally disjoint pairwise incongruent polygons all similar to P ′. It is known that there is no perfect dissection of an equilateral triangle into smaller equilateral triangles. On the other hand, an equilateral triangle has trivial perfect dissections into any number n of right triangles where n ≥ 3. We give...
متن کاملA Note on Authentication Codes
In this short note we show that the bound provided by Theorem 3.8 in 4] is not correct by exhibiting a counter example. We identify the aw in the proof of Theorem 3.8 in 4] and then we prove a correct bound on P S .
متن کاملTwo theorems on perfect codes
TWO theorems nre proved on perfect codes. The first cne states tk.at Lloyd's theorem is true without tne assumption that the number of symbols in the alphabet is a prime power. The second thevrem asser?s the impossibility of perfect group codes over non-prime-pcwer-alphabets. IA V be a finite set, I VI = q > 2, and let 1 <_ e 2 ye be Ia:ional integers. We pu?iV= (1, 2,. .. . n). Forv=(Vi)~=l E ...
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ژورنال
عنوان ژورنال: Information and Control
سال: 1975
ISSN: 0019-9958
DOI: 10.1016/s0019-9958(75)80007-6