SETI Puzzle

This problem was originally posted to the Internet newsgroups sci.crypt, sci.astro, sci.space, rec.arts.sf-lovers and rec.puzzles on August 30, 1991.

Suppose the following message was received by a radio telescope. It consists ofa number of bursts that last either one, two or three tenths of a second, indicated by S, M and L (respectively) below. The space between two bursts is either one or two tenth of a second, the longer pause marked by an X below. There are 1442 Ss, 1249 Ms, 853Ls, and 142 Xs, total time is 1018.4 sec. Can you figure out what it means?

MMMMMMMMMMMMMMMMMMMMMMMMXMMMMMMMMMMSMMMMMMMMMMMMMXMMMMMMMMMMSSMMMMMMMM
MMMMXMMMMMMMMMMSSSMMMMMMMMMMMXMMMMMMMMMMSSSSMMMMMMMMMMXMMMMMMMMMMSSSSS
MMMMMMMMMXMMMMMMMMMMSSSSSSMMMMMMMMXMMMMMMMMMMSSSSSSSMMMMMMMXMMMMMMMMMM
SSSSSSSSMMMMMMXMMMMMMMMMMSSSSSSSSSMMMMMXMMMMMMMMMMSSSSSSSSSSMMMMXMMMMM
MMMMMSSSSSSSSSSSMMMXMMMMMMMMMMSSSSSSSSSSSSMMXMMMMMSMMMMMMMMMMMMMMMMMMX
MMMMMLMMMMSMMMMMMMMMMMMMXMMMMLSMMMMSSMMMMMMMMMMMMXMMMMLLMMMMSSSMMMMMMM
MMMMXMMMLSSMMMMSSSSMMMMMMMMMMXMMMLSLMMMMSSSSSMMMMMMMMMXMMMLLSMMMMSSSSS
SMMMMMMMMXMMMLLLMMMMSSSSSSSMMMMMMMXMMLSSSMMMMSSSSSSSSMMMMMMXMMLSSLMMMM
SSSSSSSSSMMMMMXMMLSLSMMMMSSSSSSSSSSMMMMXMMLSLLMMMMSSSSSSSSSSSMMMXMMLLS
SMMMMSSSSSSSSSSSSMMXSSSMMMMXSSLMMMMSXSSLSMMMMSSXSSLLMMMMSSSXSSLSSMMMMS
SSSXSSLSLMMMMSSSSSXSSLLSMMMMSSSSSSXSSLLLMMMMSSSSSSSXSSLSSSMMMMSSSSSSSS
XSSLSSLMMMMSSSSSSSSSXSSLSLSMMMMSSSSSSSSSSXSSLSLLMMMMSSSSSSSSSSSXSSLLSS
MMMMSSSSSSSSSSSSXLLSSMSSLMSSLMMMMSSLXLLSSMSSSMSSLMMMMSSLXLLSSMSSLMSSSM
MMMSSLXLLSSMSSSMSSSMMMMSSSXLLSLMSSLMSSLMMMMSSLXLLSLMSSSMSSLMMMMSSSXLLS
LMSSLMSSSMMMMSSSXLLSLMSSSMSSSMMMMSSSXLLSMSSSMMMMSSLXLLSMSSLMMMMSSSXSSS
MLSMSLSXLLSSMSLSMSSLMMMMSSLXLLSSMSLSMSSSMMMMSSSXLLSLMSLSMSSLMMMMSSSXLL
SLMSLSMSSSMMMMSSSXLLSMSLSMMMMSSLXSLSMMMMSSSXSSLMLSMSLSXLLSSMSLSMSSLMMM
MSSLXLLSSMSLSMSSSMMMMSSLXLLSLMSLSMSSLMMMMSSLXLLSLMSLSMSSSMMMMSSSXLLSMS
LSMMMMSSSXSLSMMMMSSLXLLSSMSSLMSSLMLSMSLSMMMMSSLMLSMSLSXLLSSMSSLMSSLMLS
MSLSXSLSMMMMSSLXLLSSSMSSLMSSLMMMMSSSXLLSSSMSSSMSSLMMMMSSSXLLSSSMSSLMSS
SMMMMSSSXLLSSSMSSSMSSSMMMMSSLXLLSSMSLSMSLLMLSMSLLSXLLSMSLLSMLSMSLLLXSS
SMLSMSLSXSSSMLSMSLLXSLLSMMMMSSSXSLLLMMMMSSLXSSLMLSMSLSXSLLSMMMMSSSXSLL
LMMMMSSLXSSSMLSMSLSXSSLMLSMSLLXSLLSMMMMSSSXSLLLMMMMSSLXSSLMLSMSLSXSLLS
MMMMSSLXSLLLMMMMSSSXMLSMSLSXMLSMSLLXLLSSSMSLSMSLLMMMMSLLLXLLSSMSLSMSLL
MLSMSLLSMMLLSMSLSMLSMSLLLMMMMLLSSSMSLSMSLLMMMSLLLXLLSLMSLSMSLLMLSMSLLS
MMLLSMSLSMLSMSLLLMMMMLLSLSMSLSMSLLMMMSLLLXLLSLSMSSLMSSLMMMMSSSXLLSLSMS
SLMSSSMMMMSSSXLLSLSMSSSMSSLMMMMSSSXLLSLSMSSSMSSSMMMMSSLXLLSSMSLSMSLLML
SMSLLSMMLLSLSMSLSMSLLMLSMSLLLMMLLSLMSLLSMSLLLMLSMSLLSSMMMMLLSSLMSLSMSL
LMMMSLLSSXLLSMSLSMLSMSLLSMMLLSMSLLMLSMSLLLMMLLSLMSLSMSLLLMLSMSLLSSMMLL
SLMSLLMSLLSMLSMSLLSLMMLLSSMSLLSSMSLLSLMLSMSLLLSMMMMLLSSLMSLSMSLLMMMSLL
LSXLLSSLMSLSMSLLMLSMSLLSMMLLSLMSLSMSLLMSLLLMMMMLLLSMSLSMSLLMMMSLLSMSLL
LXLLLSMSSLMSSLMMMMSSSMSSLXLLLSMSSSMSSLMMMMSSLMSSSXLLLSMSSLMSSSMMMMSSLM
SSSXLLLSMSSSMSSSMMMMSSSMSSSXLLLSMSLSMSLLMLSMSLLLMSLLSSMMLLLSMSLLSMSLLL
MLSMSLLSLMSLLLSMMLLSSMSLLSSMSLLLSMLSMSLLLLMMMMLLLLMSLSMSLLMSLLSMMMSLLS
LMSLLLLXLLLLMSLLSMSLLSLMSLLLSMLSMSLLSSLMSLLSLLMMLLLLMSLLMSLLSSMSLLSLLM
LSMSLLSSSMSLLLSSMMLLLLMSLSMSLLLMSLLLSSMLSMSLLLLMSLLSLSMMMMLLLLMSLSMSLL
MSLLSMSLLLMSLLSSMSLLSLMSLLLSMMMSLLLLMSLLSSSMSLLSSLMSLLSLSXLLLLMSSSMSSL
MSSSMSSLMSSLMSSSMSSLMMMMSSSMSSSMSSLMSSLXLLLLMSSLMSSSMSSLMSSSMSSSMSSSMS
SLMSSSMSSSMMMMSSLMSSLMSSSMSSSMSSSXLLSSSMSLSMSLLLMLSMSLLSMMLLSSSMSLLSMS
LLMLSMSLLLMMMMLLLMSLSMSLLMMMSLLSMSLLLXSSLMLSMSLLLXLLLMSSSMSSSMMMMSSSMS
SLXLLLMSSSMSSLMMMMSSLMSSSXLLLMSSSMSSSMMMMSSLMSSSXLLLMSSLMSSSMMMMSSSMSS
LXLLLMSSSMSSSMMMMSSSMSSLXMMMMMMMMMMMMXSSSMLSSMSSLSLMMMMSSLSLXSSSMLSSMS
SLSLLSMMMMSSLSLLSXSSLSLLMLSSMSSLMMMMSSLLSSXSSLSSLMLSSMSSLMMMMSSLSLSXSS
LLSLSMLSSMSSLMMMMSSLLSLLXSSLMLSSMSSLSLMMMMSSLLSXSSLSMLSSMSSLLMMMMSSLSL
XSSLSMLSSMSSLSLMMMMSSLLLXSSLSMLSSMSSLSLSMMMMSSLLSSXSSLLSMLSSMSSLSLSMMM
MSSLSSSSXSSLSLLMLSSMSSLSSLMMMMSSLSLSSXSSLSSLSMLSSMSSLSLSMMMMSSLLLSSXSS
SMLSSMSLSMMMMSLSXSLSMLSSMSLLMMMMSLLMLSSMSLSXSLSMLSLMSLLMMMSLLSMMMMSLLM
LSSMSLLSMMMSLSXMSSLLSSMLSLMSSLSLSMMMMSSLSXSSLSLSSMLSLMSSLSSLMMMMSSLSLL
XSSLSSMLSLMSSLLMMMMSSLXSSLSMLSLMSSLMMMMSSLXSSLMLSLMSSLMMMMSSSXSSSMLSLM
SSLMMMMSSSLXSSSLMLSLMSSLMMMMSSSLSXSSSMLSLMSSLSMMMMSSSLSXSSSLSMLSLMSSLM
MMMSSSLLXSSSMLSLMSSLLMMMMSSSLLXSSSMLSLMSSLSSMMMMSSSLSSXSSSMLSLMSSLSLMM
MMSSSLSLXSSLLMMSSLSMMSSLMMSSSMMSSSLMMSSSLSMMSSSLLMMSSSLSSMMSSSLSLMMSSS
LLSMMSSSLLLMMSSSLSSSXSSLSLLMLSSMSSSLSLLMMMMSSS

Give it a try. Really. When you’re ready to look, here’s the solution.