A direct construction of 2D-CCC with arbitrary array size and flexible set size using multivariable function

Gobinda Ghosh; Nimai Sarkar; Sachin Pathak

doi:10.3934/amc.2025049

Article Contents

2026, Volume 21: 175-191. Doi: 10.3934/amc.2025049

This volume Previous Article Explicit construction of codes correcting a single reverse-complement duplication of arbitrary length Next Article Binary cyclic codes from three classes of sequences

A direct construction of 2D-CCC with arbitrary array size and flexible set size using multivariable function

1.
Mathematics Division, School of Advanced Sciences and Languages, VIT Bhopal University, Kothrikalan, Sehore, Madhya Pradesh - 466114, India
2.
School of Advance Sciences, VIT-AP University, Inavolu, 522241, Amaravati, Andhra Pradesh, India
3.
Department of Mathematics, University of Allahabad, Prayagraj, Uttar Pradesh 211002, India

^*Corresponding author: Gobinda Ghosh
^*Corresponding author: Gobinda Ghosh

Received: June 2025

Revised: September 2025

Early access: October 15, 2025

Published online: October 15, 2025

Abstract / Introduction Full Text(HTML) Figure(3) / Table(1) Related Papers Cited by

Abstract

In this paper, we propose a mathematical method for constructing two-dimensional complete complementary codes (2D-CCCs) with arbitrary array size and flexible set size. Our entire construction is based on a multivariable function (MVF). We investigate row and column sequences peak to mean envelope ratio (PMEPR) of the constructed 2D complementary codes.

Keywords:

Z- complementary code sets,
complete complementary code,
additive chareacter,
multicarrier code division multiple access.

Mathematics Subject Classification: Primary: 94A05 Secondary: 94A55.

Citation:

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Figure 1. Auto-correlation result of any set of array from $ \mathcal{G} $

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Figure 2. Cross-correlation result of any two sets of array from $ \mathcal{G} $

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Figure 3. Row and column sequence IAPR/PMEPR

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Table 1. Comparision of proposed 2D-CCC with existing works

Source	Set Size	Array Size	Based on	Constraints
[7]	$ M^{2} $	$ 2^{m}M\times2^{m}M $	$ 1 \mathrm{D}-\mathrm{CCCs} $	$ m \geq 1 $, $ M\geq 2 $
[41]	$ MK $	$ M^{2}\times K^{2} $	$ 1 \mathrm{D}-\mathrm{CCCs} $	$ M, K \geq 2 $
[6]	$ M $	$ M\times M $	BH matrices	$ M \geq 2 $
[21]	$ 2 $	$ L\times M $	Golay Sequence	$ L,\frac{M}{2} $ are complex Golay numbers
[26]	$ 2 $	$ 2^{n}\times 2^{m} $	Generalized Boolean Function	$ n,m\geq 1 $
[27]	$ 2^{k} $	$ 2^{n}\times2^{m} $	Generalized Boolean Function	$ m,n \geq k $, $ m,n,k\in\mathbb{Z}^{+} $
Theorem 3.1	$ x $	$ s_{1}\times s_{2} $	MVF	$ x=\prod_{i=1}^{a}p^{k_{i}}_{i}\prod_{j=1}^{b}q^{l_{j}}_{j}, $ $ s_{1}=\prod_{i=1}^{a}p_{i}^{m_{i}} $, $ s_{2}=\prod_{j=1}^{b}q_{j}^{n_{j}} $

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