How Can Linear Feedback Shift Registers Generate Unique Random Numbers Without Repetition?

Generating Random Numbers with No Duplicates

In pursuit of a pseudorandom number generator that yields unique numbers without repetitions, we delve into a solution that circumvents the resource-intensive methods of shuffling or checking for repeats.

Linear Feedback Shift Registers (LFSRs)

LFSRs, once implemented in hardware, offer a software-based alternative for generating non-repeating sequences. By employing a shift register and strategically XORing selected bits back into the input, LFSRs produce sequences with a length equal to the register size. For instance, a 16-bit LFSR can generate a sequence of 65,535 unique numbers.

The construction of LFSRs adheres to strict rules known as "maximal length" to ensure optimal sequence generation. These guidelines ensure that the resulting sequence possesses statistical randomness and avoids embarrassingly short or repetitive patterns.

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