Hi hed.robin,
First let's clear out something: I guess you are using RNASeq reads to quantify gene expression, am I right? If not, please specify which reads you are using and for which purpose.
I have a set of gene sequences. And some sets of reads.
Second: your "set of genes" is a multifasta containing all the gene sequences, or the transcript sequences? This changes things.
So what do you do to check if a gene is really there?
If you want to check gene expression, aligning reads against the transcript sequences or against the reference genome will generate a BAM file (or PSL if you use old programs) that you can then sort by genomic coordinate and give to a quantification algorithm (for example, HTSeq or Cufflinks). These programs count how many reads map on the gene region which is a first number that tells you if the gene is expressed (I guess you mean expressed when you say "in there").
We use read_count /(gene_length*number_of_reads_in_sample)
This sounds fair enough to me as a normalization rule. Bioinformatics is a dirty science in this context, you can always have situations like the one you described, but you have to look for the big picture. If you want to understand better why people use these normalization calculations, here is a very good article imho:
http://www.rna-seqblog.com/rpkm-fpkm-and-tpm-clearly-explained/
for some reason the reads might only map on a certain region of a gene
My PhD project is forcing me to deal with this problem. If you know which genes might show this behaviour, I strongly recommend you to do a couple of things: either running cuffdiff providing a GFF3 list of exons as "genes" (I know it's against "the rules", but works) and see for the genes you are interested in, if the expression is only on one exon and not on all the gene. Another way is to use JBrowse ( http://jbrowse.org/ ) to graphically assess where your reads map. You can easily install it in your /var/www directory and load tracks. But maybe try the first one before, it's quick and dirty but gives you an idea.
No, it is not RNAseq, it is DNA, so I guess it is sorta like lights off and on.