3 papers
cs.IT2026
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)…
cs.IT2026
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…
cs.IT2026
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…