Shifting counters

Eldert, C.; Gurk, Herbert M.; Gray, Harry J.; Rubinoff, Morris

doi:10.1109/tce.1958.6372760

Cited by 10 publications

(10 citation statements)

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“…In this section we consider the three de Bruijn sequence constructions in Group 2. The Pref-same [3,9,12] and the Pref-opposite [2] are greedy constructions based on the last bit of the sequence as it is constructed. They have the downside of requiring an exponential amount of memory.…”

Section: Algo Ccr3mentioning

confidence: 99%

“…• n = 6: (0,1,2), (3,4), (5,6) • n = 7: (0,1), (2,3), (4,5), (6,7) • n = 8: (0,1,2), (3,4), (5,6), (7,8) • n = 9: (0,1), (2,3), (4,5), (6,7), (8,9) before joining them together one at a time. Note when n = 9, strings with weights 4 and 5 are grouped together before the smaller cycles are joined together.…”

Section: Weight Range Constructionsmentioning

confidence: 99%

“…It is possible, however, to tweak the cool-lex implementation so the discrepancies are equivalent. For instance for n = 9, the smaller cycles with weights (0, 1, 2), (3,4), (5,6), (7,8,9) could be joined together instead.…”

Section: Weight Range Constructionsmentioning

confidence: 99%

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Investigating the discrepancy property of de Bruijn sequences

Gabric¹,

Sawada²

2020

Preprint

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The discrepancy of a binary string refers to the maximum (absolute) difference between the number of ones and the number of zeroes over all possible substrings of the given binary string. We provide an investigation of the discrepancy of known simple constructions of de Bruijn sequences. Furthermore, we demonstrate constructions that attain the lower bound of Θ(n) and a new construction that attains the previously known upper bound of Θ( 2 n √ n ). This extends the work of Cooper and Heitsch [Discrete Mathematics, 310 (2010)].

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Section: Algo Ccr3mentioning

confidence: 99%

Section: Weight Range Constructionsmentioning

confidence: 99%

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Investigating the discrepancy property of de Bruijn sequences

Gabric¹,

Sawada²

2020

Preprint

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“…Let the order m of the cyclic group G be expressed as the product m = m 1 m 2 m k of k factors that are pairwise relatively prime. We want the residues r i = L mod m i ; 1 i k : (7) The Chinese remainder theorem says that there is exactly one value of L in 0 : : :m ? 1] that satis es the simultaneous equations 7:…”

Section: Count Recovery With Discrete Logarithmsmentioning

confidence: 99%

“…Using a linear feedback shift register, or LFSR, is an extremely attractive way to generate a sequence of binary words: a single two-input exclusive-OR gate is often the only extra logic needed to make a shift register generate, by successive shifts, all of its possible nonzero values. Applications of LFSRs include error-correcting codes 1, 21,22], pseudorandom sequence generation for ranging and synchronization 11], test-pattern generation and signature analysis in VLSI circuits 16], and program counters in simple computers 7,19].…”

Section: Introductionmentioning

confidence: 99%

Maximal and near-maximal shift register sequences: efficient event counters and easy discrete logarithms

Clark

Weng

1994

IEEE Trans. Comput.

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A Linear Feedback Shift Register, or LFSR, can implement an event counter by shifting whenever an event occurs. A single two-input exclusive-OR gate is often the only additional hardware necessary to allow a shift register to generate, by successive shifts, all of its possible nonzero values. The counting application requires that the number of shifts be recoverable from the LFSR contents so that further processing and analysis may be done. Recovering this number from the shift register value corresponds to a problem from number theory and cryptography known as the discrete logarithm. For some sizes of shift register, the maximal-length LFSR implementation requires more than a single gate, and for some the discrete logarithm calculation is hard. This paper proposes for such sizes the use of certain one-gate LFSRs whose sequence lengths are nearly maximal, and which support easy discrete logarithms. These LFSRs have a concise mathematical characterization, and are quite common. The paper concludes by describing an application of these ideas in a computer hardware monitor, and by presenting a table that describes e cient LFSRs of size up to 64 bits.

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