Abstract Firstly, we give a formula on the generalized Hamming weight of linear codes constructed generically by defining sets. Secondly, by choosing properly the defining set we obtain a class of cyclotomic linear codes and then present two alternative formulas to calculate their generalized Hamming weights. Lastly, we determine their weight distribution and generalized Hamming weights partial...

We analyze in detail the performance of a Hamming network classifying inputs that are distorted versions of one of its m stored memory patterns. The activation function of the memory neurons in the original Hamming network is replaced by a simple threshold function. The resulting Threshold Hamming Network (THN) correctly classifies the input pattern, with probability approaching 1, using only O...

In this paper, we introduce generalized extended Hamming codes over Galois rings GR(2,m) of characteristic 2 with extension degree m. Furthermore we prove that the minimum Hamming weight of generalized extended Hamming codes over GR(2,m) is 4 and the minimum Lee weight of generalized extended Hamming codes over GR(8,m) is 6 for all m ≥ 3. ——————————————————————– ———Received May 25, 2011. This w...

A k-bit Hamming prefix code is a binary code with the following property: for any codeword x and any prefix y of another codeword, both x and y having the same length, the Hamming distance between x and y is at least k. Given an alphabet A = [a1, . . . , an] with corresponding probabilities [p1, . . . , pn], the k-bit Hamming prefix code problem is to find a k-bit Hamming prefix code for A with...

In this paper, we present a class of low-hit-zone (LHZ) frequency hopping sequence set (LHZ FHS set) with periodic partial Hamming correlation property from the Cartesian product of known FHS sets. It is shown that the sequence set is near optimal with respect to the partial Hamming correlation bound of the LHZ FHS set. Keywords-frequency hopping sequence set; periodic partial Hamming correlati...

Frequency hopping sequences (FHSs) with favorable partial Hamming correlation properties have important applications in many synchronization and multiple-access systems. In this paper, we investigate constructions of FHSs and FHS sets with optimal partial Hamming correlation. We first establish a correspondence between FHS sets with optimal partial Hamming correlation and multiple partition-typ...

The Hopfield model neural net has attracted much recent attention. One use of the Hopfield net is as a highly parallel content-addressable memory, where retrieval is possible although the input is corrupted by noise. For binary input patterns, an alternate approach is to compute Hamming distances between the input pattern and each of the stored patterns and retrieve that stored pattern with min...

In this paper the effect of window shape parameter „α‟ in Kaiser-Hamming and Cosh-Hamming window functions on the signal to noise ratio (SNR) values of the Indian Mesosphere-Stratosphere-Troposphere (MST) radar is computed. The six parts of multibeam observations of the lower atmosphere made by the MST radar are utilized for the analysis of results. Prior to the Fourier transformation, the in-p...