Beniamin Mounits

Improved upper bounds on sizes of codes

Let A(n,d) denote the maximum possible number of codewords in a binary code of length n and minimum Hamming distance d. For large values of n, the best known upper bound, for fixed d, is the Johnson bound. We give a new upper bound which is at least as good as the Johnson bound for all values of n and d, and for each d there are infinitely many values of n for which the new bound is better than the Johnson bound. For small values of n and d, the best known method to obtain upper bounds on A(n,d) is linear programming. We give new inequalities for the linear programming and show that with these new inequalities some of the known bounds on A(n,d) for n/spl les/28 are improved.

Quasi-perfect codes with small distance

The main purpose of this paper is to give bounds on the length of the shortest and longest binary quasi-perfect codes with a given Hamming distance, covering radius, and redundancy. We consider codes with Hamming distance 4 and 5 and covering radius 2 and 3, respectively. We discuss the blockwise direct sum (BDS) construction which has an important role in finding these bounds.

New upper bounds on codes via association schemes and linear programming

An optical receiver especially useful for digital fiber optic systems operating a high pulse rates, converts the pulsed current signal generated by a PIN diode into a pulsed voltage utilizing a current to voltage converter comprising an FET input transistor, a complimentary cascoded bipolar transistor, and a large feedback resistor to reduce noise while providing a wide band width and dynamic range. The pulsed voltage signal is amplitude limited in a limiting amplifier and passed through a low pass filter to remove excess bandwidth and further reduced noise before being applied to a high speed comparator which generates the digital output. The pulsed voltage signal is passed from the current to voltage converter to the limiting amplifier through an emitter follower coupling transistor to isolate the open loop gain of the current to voltage converter so that its band width will not be changed with load.

New upper bounds for nonbinary codes

New upper bounds on codes are presented. The bounds are obtained by linear and semidefinite programming.

Quasiperfect codes with small distance

The main purpose of this paper is to give bounds on the length of the shortest and longest binary quasiperfect codes with a given Hamming distance, covering radius, and redundancy. We consider codes with Hamming distance 4 and 5 and covering radius 2 and 3, respectively.

Improvement on the Johnson upper bound for error-correcting codes

Let A(n, d) denote the maximum possible number of codewords in a binary code of length n and minimum Hamming distance d. For large values of n the best known upper bound, for fixed d, is the Johnson bound. We give a new upper bound which is at least as good as the Johnson bound for all values of n and d, and for each d there are infinitely many values of n for which the new bound is better than the Johnson bound.

New upper bounds on A(n, d)

Upper bounds on the maximum number of codewords in a binary code of a given length and minimum Hamming distance are considered. New bounds are derived by a combination of linear programming and counting arguments. Some of these bounds improve on the best known analytic bounds. Several new record bounds are obtained for codes with small lengths