15 papers
Binary Multiple-Node-Erasure-Correcting Codes over Complete Graphs: Constructions, q-Ary Metric Balls, and Duality
Aryeh Lev Zabokritskiy
We study linear codes whose coordinates are the ordinary edges and self-loops of complete undirected graphs; a node erasure removes all coordinates incident with a failed vertex. T…
Coding for Multiple Reverse-Complement and Palindromic Duplications
Aryeh Lev Zabokritskiy
Reverse-complement (RC) and palindromic (PAL) duplications copy a length- block, reverse the copy, and insert it next to the original block; an RC duplication also complements t…
Prescribed-Difference Matchings with Four and Eight Holes: Fourier Filters for Compatible Boundaries
Avraham Kreindel, Aryeh Lev Zabokritskiy
Let and let have sum zero. The prescribed-difference matching problem asks whether can be partitioned into pairs w…
Correcting Connectivity in Arc-Based QUBO Models for Fixed-Fleet Vehicle Routing
Omer Gurevich, Maor Matityahu, Tal Mor +1
We revisit a degree-only arc Hamiltonian for fixed-fleet, homogeneous, uncapacitated vehicle routing. Because its local penalties define only a cycle cover, ground states may conta…
Quantitative tiling stability from quadratic discrepancy in Hamming spaces
Valery, Grishin, Aryeh Lev Zabokritskiy
Quadratic ball discrepancy defines an energy on codes in finite Hamming spaces. At perfect-code parameters, its exact minimizers are the perfect codes. We fix the alphabet size, le…
Asymptotically Tight Bounds for Generalized Covering Radii of Binary Primitive BCH Codes at All Higher Orders
Zeev Vladimir Belinsky, Aryeh Lev Zabokritskiy
We study how few parity-check columns are needed to span several prescribed syndromes of a binary primitive BCH code of length , where is the extension degree. For the f…