Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.24019

Explicit construction of optimal binary linear complementary pairs via Belov codes

Yansheng Wu·Jing Chen·Jong Yoon Hyun
View original source ↗Read source document ↗Export metadata ↓

Abstract

The study of linear complementary pairs (LCPs) has been a hot topic in coding theory. Recently, Güneri constructed an infinite family of optimal binary LCPs from Solomon-Stiffler codes. Specifically, he proved that for every $k \geq 5$ and $d \geq \lceil (k - 1)/2 \rceil 2^{k - 1}$, there exist optimal binary linear complementary pairs of codes of length $g_2(k,d)$, where $g_2(k,d)$ denotes the Griesmer bound. In this paper, we construct additional optimal binary LCPs from Belov codes, which form a generalized class of Solomon-Stiffler codes. Our results not only generalize Güneri's construction, but also enable more flexible construction of optimal binary LCPs with a wide range of minimum distances.

Explore related subjects

cs.ITmath.IT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Yansheng Wu, Jing Chen, Jong Yoon Hyun. 2026-10-16. Explicit construction of optimal binary linear complementary pairs via Belov codes. https://arxiv.org/abs/2610.24019

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Reed-Solomon Codes with Optimal Repair Bandwidth: A Basis-Transformation Approach

Maximum distance separable (MDS) codes are widely used in distributed storage, but naively repairing a single failure in an $(n,k)$ MDS code requires downloading the full contents of $k$ surviving nodes. Minimum storage regenerating (MSR) codes, introduced by Dimakis et al., minimize repair bandwidth while preserving the MDS property by contacting $d>k$ helper nodes and downloading only a fraction of each helper. For scalar MDS codes, Guruswami and Wootters established a linear repair framework, and Tamo, Ye, and Barg subsequently gave the first explicit Reed-Solomon (RS) codes achieving the MSR point. Their construction yields RS-MSR codes with subpacketization $\ell=s\prod_{i=1}^n p_i$, where $s=d+1-k$ and the distinct primes $p_i$ satisfy $p_i\equiv 1\pmod{s}$. In this paper, we show that this congruence condition is not intrinsic to the RS repair problem. We develop a basis-transformation approach to the construction of repair-enabling subspaces. The approach consists of three deterministic operations -- Euclidean Square Partition, Transposition, and Column Aggregation -- which construct the required repair-enabling subspaces directly from the standard monomial basis of the repair field. Consequently, we obtain RS-MSR codes with subpacketization $\ell=s\prod_{i=1}^n p_i$ for arbitrary distinct primes $p_i>s$. For fixed $s$, this improves the subpacketization of the Tamo--Ye--Barg construction by a factor asymptotic to $φ(s)^{n+\mathrm{o}(n)}$, where $φ(\cdot)$ denotes Euler's totient function.

cs.IT↗
arXiv2026

Derivation Depth as an Information Metric: Axioms, Coding Theorems, and Storage--Computation Tradeoffs

We introduce derivation depth-a computable metric of the reasoning effort needed to answer a query based on a given set of premises. We model information as a two-layered structure linking abstract knowledge with physical carriers, and separate essential core facts from operational shortcuts. For any finite premise base, we define and prove the computability of derivation depth. By encoding reasoning traces and applying information-theoretic incompressibility arguments, we establish fundamental bounds linking depth to the descriptive complexity of queries. For frequently asked, information-rich queries, the minimal description length grows proportionally to depth times the logarithm of the knowledge base size. This leads to a practical storage-computation tradeoff: queries accessed beyond a critical threshold become cheaper to cache than recompute. We formulate optimal cache allocation as a mathematical optimization problem solvable with approximation guarantees and extend the framework to handle noisy or incomplete knowledge bases.

cs.IT↗
arXiv2026

Insertion Correcting Capability for Quantum Deletion-Correcting Codes

It is conjectured that a quantum code $C$ corrects $t$ deletion errors if and only if $C$ corrects a total of $t$ insertion and deletion errors. Although this conjecture has been proved only under certain conditions, it has not been proved in general. In this paper, we prove this conjecture for general quantum codes. Specifically, we show that a quantum state after an insertion error is represented as a product state of the original multi-qudit system and the inserted quantum state. Then, we prove this conjecture by combining the previous results and this property. In addition, we define generalized insertion errors by removing the quantum channel requirement from insertion errors and present their properties.

cs.IT↗