From the 2 of 8 linked papers with an AI index.
8 papers
The Exact Second Generalized Covering Radius of Binary Primitive Triple-Error-Correcting BCH Codes
Isaac Barouch Essayag, Aryeh Lev Zabokritskiy
Let be the binary primitive triple-error-correcting BCH code of length . We determine its second generalized covering radius exactly: $R_2(C_m)…
Perfect codes as exact minimizers of quadratic discrepancy in q-ary Hamming spaces
Aryeh Lev Zabokritskiy
Stolarsky's invariance principle converts quadratic discrepancy into an energy-minimization problem. Barg developed its form for binary Hamming space and proved that binary perfect…
Extinction Depth and q-ary Error-Correcting Codes for the Limited Permutation Channel
Noam Ben Shimon, Aryeh Lev Zabokritskiy
In the radius-one limited permutation channel, errors consist of disjoint adjacent transpositions. A correcting code must separate distinct codewords: their error balls may not con…
Independent Sets in Multiset Profile Graphs via Weighted Local Covers
Aryeh Lev Zabokritskiy
The paper studies independent sets in unit‑transfer graphs defined on multiset profiles, introducing weighted local covers to prove the prime‑checksum conjecture for the next odd p…
Multiset Deletion Codes: Cyclic Constructions, Bounds, and Exact Results
Avraham Kreindel, Isaac Barouch Essayag, Aryeh Lev Zabokritskiy
The paper investigates deletion‑correcting codes for multisets over a q‑ary alphabet, providing a cyclic Sidon‑type construction with low redundancy and linear‑time decoding, and d…
Perfect Matchings with Prescribed Differences Beyond Hall: The Two-Hole Problem
Aryeh Lev Zabokritskiy
The Balister--GyÅri--Schelp (BGS) conjecture asks whether every zero-sum list of nonzero vectors in is the prescribed-difference profile of a perfect ma…