This sounds like an electronic replacement of the jacquard punched cards used in knitting looms.

If I am to understand the problem correctly - the data is fixed width at 25 bits, but you may want to insert/delete rows. The simplest method of handling this is a singularly linked list as described by Anil Gupta. Get a book on computer science algorithms and this will describe a linked list for you. For such a linked list, each record consists of the row data and the address of the next entry. This means you rows can exist in memory in any order but you read the data out in order due to the address field. By manipulating the address fields in the records you can re-arrange (add/delete) the data list any way you see fit.Also you might want to add a count field as it is common for the same row data to exist in a sequence - this will save you repeating the data records - thus saving some memory.
You can have multiple 'chains' for different patterns if you wish - you only need to know the starting address. Free entries might have an address value of -1 to say they're available.

It's easier done on the PC side - in fact C++ with the STL has a prebuilt structure for this. Nevertheless, a linked list is easy to code even in assembler (I've done it many times).