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This paper presents binary phase codes and corresponding decoding filterswhich are optimal in the sense that they produce no sidelobes and theymaximise the signal-to-noise ratio (SNR henceforth). The search is madeby investigating all possible binary phase codes with a given length.After selecting the code,  the first step is to find a filter whichproduces no sidelobes.  This is possible for all codes with no zeros inthe frequency domain, and it turns out that most codes satisfy thisrequirement. An example of a code which cannot be decoded in this way isa code with a single phase, i.e. a long pulse. The second step is toinvestigate the SNR performance of the codes. Then the optimal code of agiven length is the one with the highest SNR at the filter output. Allcodes with lengths of 3–25 bits were studied, which means investigating33554428  binary phase codes. It turns out that all Barker codes exceptthe 11-bit code are optimal in the above sense. It is well known that theperformance of matched-filter decoding of Barker codes  is better thandecoding without sidelobes.   In the case of  the 7-bit Barker code,  itis shown here that the SNR given by sidelobe-free decoding is nearly30% worse than that of standard decoding, but for the 13-bit codesidelobe-free decoding is only about 5% worse. The deterioration of SNRshould be evaluated against the benefits gained in disposing of thesidelobes, which, even for  the 13-bit code, contribute by 7.1% to thetotal signal power from a homogeneous target. Thus, regions of weakscattering can be contaminated by the sidelobes  from neighbouring layersof strong scattering, causing broadening of thin spatial structures andgiving a lower spatial resolution than implied by the bit length. Apractical example is shown where sidelobes mask a weak signal when thestandard matched filter is used in the analysis. An improvement isachieved when sidelobe-free filtering is carried out.  <b>Key words.</b> Radio science (ionospheric physics; signal processing;instruments and techniques

Optimal binary phase codes and sidelobe-free decoding filters with application to incoherent scatter radar