Good cyclic codes and the uncertainty principle

S Evra, E Kowalski, A Lubotzky

Research output: Contribution to journalArticlepeer-review


A long standing problem in the area of error correcting codes asks whether there
exist good cyclic codes. Most of the known results point in the direction of a negative answer.
The uncertainty principle is a classical result of harmonic analysis asserting that given a non-zero function f on some abelian group, either f or its Fourier transform f has large support.
In this note, we observe a connection between these two subjects. We point out that even a weak version of the uncertainty principle for fields of positive characteristic would imply that good cyclic codes do exist. We also provide some heuristic arguments supporting that this is indeed the case.
Original languageEnglish
Pages (from-to)305-332
Number of pages28
JournalEnseignement Mathematique
Issue number3-4
StatePublished - 4 Sep 2018


  • Artin conjecture
  • Cyclic codes
  • Finite abelian groups
  • Primitive roots
  • Uncertainty principles


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