REVIEW
On the MacWilliams Theorem over Codes and Lattices
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
read the original abstract
Analogies between codes and lattices have been extensively studied for the last decades, in this dictionary, the MacWilliams identity is the finite analog of the Jacobi-Poisson formula of the Theta function. Motivated by the random theory of lattices, the statistical significance of MacWilliams theorem is considered, indeed, MacWilliams distribution provides a finite analog of the classical Gauss distribution. In particular, the MacWilliams distribution over quotient space of a code is statistical close to the uniform distribution. In the respect of lattices, the analogy of MacWilliams identity associated with nu-function was conjectured by Sole in 1995. We give an answer to this problem in positive.
Discussion (0). Continue with ORCID to comment.