Review of Algebraic Shift Register Sequences by Mark Goresky and Andrew Klapper

Click to increase image sizeClick to decrease image size

Notes

¹Not everyone defined the autocorrelation this way, but this definition is useful for sequences of elements in GF(2).

²The Berlekamp-Massey algorithm allows one to determine the connection polynomial of an LFSR sequence of period 2 ^r  − 1 with only 2r terms of the sequence.

³Usually, p-adic digits are written in the order of least significant on the left to most significant on the right, as one usually writes real numbers represented as decimals. Here, to match the ordering of the sequence of coefficients used in cryptographic applications, we have reversed the ordering as presented by Sage and removed the radix (“decimal”) point.

This article not subject to United States copyright law.

Additional information

Notes on contributors

David Joyner

David Joyner is a professor at the U.S. Naval Academy.