I'm looking for a book containing the statistics of random linear code. By "random" I mean that the parity matrix (or the generating matrix) of the code is taken at random with uniform distribution from the appropriate set of matrices, and by "statistics" I mean things like concentration inequalities for the minimum weight of the random code, or results on the distribution of the weights of the codewords.
Although these kind of results are well known, I was not able to find a reference book. Instead, I keep finding unpublished lectures notes or published papers with only partial results (see Note 1). (I need a book reference to cite in a publication.)
Thanks for any help
Note 1. By "partial results" I mean that the papers I find do not cover the whole subject and provide only special cases. Moreover, each paper have different notation, and more or less different assumptions, so I cannot just cite them but I have to provide a quite long translation and adaptation for the reader. If I'll have a single book on the subject, with uniform notation and assumptions, it would be much better. As an analogy, if I need any basic result of Algebra, I can pick among hundreds of introductory books on Algebra (say Lang's undergraduate algebra) as a reference. Isn't there a similar book on error-correcting codes with a chapter on random linear codes?
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$\begingroup$ I suspect this is a XY problem; you are perfectly free to cite lecture notes, published papers, etc. in a publication. There are lots and lots of true facts that are not stated in any book. $\endgroup$D.W.– D.W. ♦2025年01月27日 18:22:09 +00:00Commented Jan 27 at 18:22
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$\begingroup$ I agree with the other comment, perhaps give us a result from a paper that you think is "partial", just for guidance. $\endgroup$kodlu– kodlu2025年01月29日 07:16:58 +00:00Commented Jan 29 at 7:16
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$\begingroup$ @D.W. Each time I cited a result from lecture notes, I was rightly asked by the referees to use another reference, since: 1) lecture notes have not been peer-reviewed, 2) lecture notes are stored on professors' personal websites and can disappear any moment. Regarding citing published papers, I'll expand my question explaining what I mean by "partial results." $\endgroup$en-drix– en-drix2025年01月29日 08:58:56 +00:00Commented Jan 29 at 8:58