Isaac Barouch Essayag

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cs.IT2026

The Exact Second Generalized Covering Radius of Binary Primitive Triple-Error-Correcting BCH Codes

Isaac Barouch Essayag, Aryeh Lev Zabokritskiy

Let $C_{m} = BCH (3, m)$ be the binary primitive triple-error-correcting BCH code of length $2^{m} - 1$ . We determine its second generalized covering radius exactly: $R_2(C_m)…

cs.IT2026

Polynomial Constructions and Deletion-Ball Geometry for Multiset Deletion Codes

Avraham Kreindel, Isaac Barouch Essayag, Aryeh Lev Zabokritskiy

We study error-correcting codes in the space $S_{n, q}$ of length- $n$ multisets over a $q$ -ary alphabet under the deletion metric, motivated by permutation channels in whi…

cs.IT2026

Multiset Deletion Codes: Cyclic Constructions, Bounds, and Exact Results

Avraham Kreindel, Isaac Barouch Essayag, Aryeh Lev Zabokritskiy

We study deletion-correcting codes in the space of length- $n$ multisets over a $q$ -ary alphabet. We present an explicit cyclic Sidon-type construction for arbitrary alphabet size $…

cs.IT2025

Optimal Functional $2^{s - 1}$ -Batch Codes: Exploring New Sufficient Conditions

Lev Yohananov, Isaac Barouch Essayag

A functional $k$ -batch code of dimension $s$ consists of $n$ servers storing linear combinations of $s$ linearly independent information bits. These codes are designed to recover a…

The Exact Second Generalized Covering Radius of Binary Primitive Triple-Error-Correcting BCH Codes

Polynomial Constructions and Deletion-Ball Geometry for Multiset Deletion Codes

Multiset Deletion Codes: Cyclic Constructions, Bounds, and Exact Results

Optimal Functional 2s−1-Batch Codes: Exploring New Sufficient Conditions

Optimal Functional $2^{s - 1}$ -Batch Codes: Exploring New Sufficient Conditions