Editing Maximum length sequence (section)

{{Short description|Type of pseudorandom binary sequence}}
{{Use American English|date = March 2019}}
A '''maximum length sequence''' ('''MLS''') is a type of [[pseudorandom binary sequence]].

They are bit sequences generated using maximal [[linear-feedback shift register]]s and are so called because they are [[periodic function|periodic]] and reproduce every [[binary sequence]] (except the zero vector) that can be represented by the shift registers (i.e., for length-''m'' registers they produce a sequence of length 2<sup>''m''</sup>&nbsp;&minus;&nbsp;1). An MLS is also sometimes called an '''n-sequence''' or an '''m-sequence'''. MLSs are [[Frequency spectrum|spectrally flat]], with the exception of a near-zero DC term.

These sequences may be represented as coefficients of irreducible polynomials in a [[polynomial ring]] over [[Congruence subgroup|Z/2Z]].

Practical applications for MLS include measuring [[impulse response]]s (e.g., of room [[reverberation]] or arrival times from towed sources in the ocean<ref>{{Cite journal |last1=Gemba |first1=Kay L. |last2=Vazquez |first2=Heriberto J. |last3=Fialkowski |first3=Joseph |last4=Edelmann |first4=Geoffrey F. |last5=Dzieciuch |first5=Matthew A. |last6=Hodgkiss |first6=William S. |date=October 2021 |title=A performance comparison between m-sequences and linear frequency-modulated sweeps for the estimation of travel-time with a moving source |url=https://asa.scitation.org/doi/10.1121/10.0006656 |journal=The Journal of the Acoustical Society of America |language=en |volume=150 |issue=4 |pages=2613–2623 |doi=10.1121/10.0006656 |pmid=34717519 |bibcode=2021ASAJ..150.2613G |s2cid=240355915 }}</ref>). They are also used as a basis for deriving pseudo-random sequences in digital communication systems that employ [[direct-sequence spread spectrum]] and [[frequency-hopping spread spectrum]] [[transmission system]]s, and in the efficient design of some [[Functional magnetic resonance imaging|fMRI]] experiments.<ref name="buracas">{{cite journal |author=Buracas GT, Boynton GM |title=Efficient design of event-related fMRI experiments using M-sequences |journal=NeuroImage |volume=16 |issue=3 Pt 1 |pages=801–13 |date=July 2002 |pmid=12169264 |doi=10.1006/nimg.2002.1116 |s2cid=7433120 }}</ref>