The proliferation of the SARS-CoV-2 virus to the whole world caused more than 250,000 deaths worldwide and over 4 million confirmed cases. The severity of Covid-19, the exponential rate at which the virus proliferates, and the rapid exhaustion of the public health resources are critical factors. The RT-PCR with virus DNA identification is still the benchmark Covid-19 diagnosis method. In this work we propose a new technique for representing DNA sequences: they are divided into smaller sequences with overlap in a pseudo-convolutional approach, and represented by co-occurrence matrices. This technique analyzes the DNA sequences obtained by the RT-PCR method, eliminating sequence alignment. Through the proposed method, it is possible to identify virus sequences from a large database: 347,363 virus DNA sequences from 24 virus families and SARS-CoV-2. Experiments with all 24 virus families and SARS-CoV-2 (multi-class scenario) resulted 0.822222 ± 0.05613 for sensitivity and 0.99974 ± 0.00001 for specificity using Random Forests with 100 trees and 30% overlap. When we compared SARS-CoV-2 with similar-symptoms virus families, we got 0.97059 ± 0.03387 for sensitivity, and 0.99187 ± 0.00046 for specificity with MLP classifier and 30% overlap. In the real test scenario, in which SARS-CoV-2 is compared to Coronaviridae and healthy human DNA sequences, we got 0.98824 ± 0.01198 for sensitivity and 0.99860 ± 0.00020 for specificity with MLP and 50% overlap. Therefore, the molecular diagnosis of Covid-19 can be optimized by combining RT-PCR and our pseudo-convolutional method to identify SARS-CoV-2 DNA sequences faster with higher specificity and sensitivity.