Some New Optimum Golomb Rectangles

Some New Optimum Golomb Rectangles

We give some new optimumGolomb rectangles found by computer search. AMS Subject Classi cation. 05B99 In [2] Robinson de ned a Golomb rectangle as an N M array of ones and zeros such that the two-dimensional autocorrelation has three values: 0; 1 and K, where K is the number of ones in the array. This means that the positions of the ones in any nonzero integral translation of the rectangle will ...

Some new optimum Golomb rulers

0 Theorem 4, unlike Theorem 2, is not a s'pecial case of a known general result: it is not known if the statement of Theorem 4 holds for twoaccess channels that are not pairwise reversible. There is a converse to Theorem 4: For any fixed rate strictly inside R o , there exists a code with that rate for which X I 1 + o(N). This result holds for general twoaccess channels, and is proved by random...

Golomb rectangles as folded rulers

On the Design of Optimum Order 2 Golomb Ruler

A Golomb ruler with M marks can be defined as a set {ai} of integers so that all differences δij = aj − ai, i 6= j, are distinct. An order 2 Golomb ruler is a Golomb ruler such that all differences δijk` = |δk` − δij |, {i, j} 6 = {k, `}, are distinct as much as possible. Contruction of optimum order 2 Golomb ruler, i.e., of rulers of minimum length, is a highly combinatorial problem which has ...

Simulation and Analysis of Optimum Golomb Ruler Based 2D Codes for OCDMA System

The need for high speed communications networks has led the research communities and industry to develop reliable, scalable transatlantic and transpacific fiber-optic communication links. In this paper the optimum Golomb ruler based 2D OCDMA codes has been demonstrated. An OCDMA system based on the discussed 2D codes is designed and simulated on Optisystem. The encoder and decoder structure of ...