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In ROLLO - Rank-Ouroboros, LAKE & LOCKER, Ideal codes are defined in Definition 2.1.4. Thanks to the Lemma 1, it is proved that every block of ideal matrix is non-singular.

Now, why do they say "hence C can be represented under systematic form"? And in the page 11, I read "indeed, the parity-check matrix under systematic form of C if of the form..." Why has H this form?

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  • $\begingroup$ Are you asking generically why non-singular matrices have systematic forms, or why a block matrix with non-singular blocks has a systematic form? $\endgroup$ – Mark Jul 8 '20 at 18:34
  • $\begingroup$ @Mark Why a block matrix with non-singular blocks has a systematic form? Thanks. And why the systematic parity check matrix has that form. $\endgroup$ – Paul Jul 9 '20 at 7:11
  • $\begingroup$ Can anyone help me? $\endgroup$ – Paul Aug 19 '20 at 10:47
  • $\begingroup$ @Paul I'm not sure, but the authors may be very happy to explain it if you'd send an email to them. $\endgroup$ – DannyNiu Sep 28 '20 at 2:35

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