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In the article Womcodes constructed with projective geometries Frans Merkx constructed several good wom-codes (write-once memory codes, see How to reuse a "write-once" memory by Rivest & Shamir for classical introduction). But the code $\left< 15\right>^7/15$ (which allows to write 7 times a number from 1 to 15 in 15 write-once bit positions (wits)) was described without any technical details. The author refers to his report F. Merkx, Codes for Write-Once Memories, Rapport Interne, Ecole Nationale Superieure des Telecommunications, Paris, 1984 which is not available online.

Are there any books or articles containing detailed description of the code $\left< 15\right>^7/15$?

This is the link to French library containing Merxk's report but unfortunately it is out of reach for me.

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  • $\begingroup$ I saw a lecture which described how to use a Fano plane for this problem with smaller parameters. It feels like a projective plane would be used for this problem. Gerhard "Is Struggling To Remember Parameters" Paseman, 2019.08.23. $\endgroup$ Commented Aug 23, 2019 at 15:44
  • $\begingroup$ @GerhardPaseman This case corresponds to projective space $PG(3,2)$. Fano plane gives $⟨7⟩^3/7$-wom-code, it is clear. The code $⟨15⟩^7/15$ can be implemented in different ways. It would be interesting to compare our algorithms with original Merkx's approach. $\endgroup$ Commented Sep 24, 2019 at 7:13
  • $\begingroup$ the library link you added says "Communicable sur demand" --- suggesting you can just ask for a copy... $\endgroup$ Commented Sep 28, 2019 at 8:23
  • $\begingroup$ @CarloBeenakker It is not clear how can I do it. Probably I'll write on their email. $\endgroup$ Commented Sep 28, 2019 at 8:28

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