Can random mutations cause an increase in information in the genome?

OK i'm a highschool student so I may not be as knoladgeable or (have verry good spelling) but all you guys seam to be doing is fighting over the meaning of his question, here is a general answer that I hope someone who is more specialized in that field can run with,an information gain is often said to be an impossible or rare event in the occorance of random mutation, this is simply not true. Many complex organisms have more than one of a spacific gene, when one of these genes is mutated to serv a diferent functuon that turns out to be benificial the next generation ends up with both the normal extra copeys of the genes origonally mutated pluss the gene that serves a seperate perpose... this is an information gain it it not?

what I got from the new posts is that CS is simply a shorthand for genetic material or the spacific segments of DNA that are being discussed, I dont understand why you want an explonation for this...also you people get way too technical with the term random, its an impossible mathmatical function shorthandedly used to defign something that has so many variables involved with the outcome that it wuld be inpractical if not impossible at the given time to attempt to calculate especially if the model works, simply useing a random variable, like someone who i've now forgotten said, when you flip a coin there is an arguably infinate or extensively long chain of events leading up to it with factors that are only existant currently as their spread out effect

sorry i responded wile you guys did exactly wat I was explaining