Author

V. Grishin

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Preprint Sep 2026

Systematic Codes Correcting Two Deletions with Three Redundant Symbols over Large Alphabets

We construct systematic $q$-ary codes correcting two deletions with three redundant symbols over polynomial-size alphabets. For every information length $n\ge2$, our first construction has length $n+3$ over an alphabet of size $q=2^s<2^{32}n^7$ for some integer $s$, with polynomial-time encoding and decoding. A cardina...

V. Grishin, Aryeh Lev Zabokritskiy · 0 citations

Preprint Aug 2026

Quantitative tiling stability from quadratic discrepancy in Hamming spaces

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, length, and code cardinality and compare all codes with these parameters. We prove tiling-defect stability: excess discrepancy above the perfe...

V. Grishin, Aryeh Lev Zabokritskiy · 0 citations