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Published January 2014 | public
Book Section - Chapter

Tree Codes and a Conjecture on Exponential Sums


We propose a new conjecture on some exponential sums. These particular sums have not apparently been considered in the literature. Subject to the conjecture we obtain the first effective construction of asymptotically good tree codes. The available numerical evidence is consistent with the conjecture and is sufficient to certify codes for significant-length communications.

Additional Information

Copyright is held by the owner/author(s). Publication rights licensed to ACM. C.M. is supported by NSF grants CCF-1117426 and CCF- 1219117, and ARO contract W911NF-04-R-0009. L.J.S. is supported by NSF grant CCF-1038578. Many students' branch and bound implementations were very successful (23 students crossed the ℓ = 100 threshold); we thank all for their dedication and enthusiasm. Specific results are cited with permission. We also thank Alex Russell and Anup Rao for helpful discussions.

Additional details

August 22, 2023
October 26, 2023