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A Costas array of size *n* is an *n* × *n* binary matrix such that no two of the $inom{n}{2}$ line segments connecting 1s have the same length and slope. Costas arrays are found by finite-field-based construction methods and their manipulations (systematically constructed) and exhaustive search methods. The arrays found exhaustively, which are of completely unknown origin, are called sporadic. Most studies in Costas arrays have tended to focus on systematically constructed Costas arrays rather than sporadic ones, which reveals the hardness of examining a link between systematically constructed Costas arrays and sporadic ones. This paper introduces a new transformation that preserves the Costas property for some Costas arrays, but not all. We observed that this transformation could transform some systematically constructed Costas arrays to sporadic ones and vice versa. Moreover, we introduce a family of arrays with the property that the auto-correlation of each array and the cross-correlation between any two arrays in this family is bounded above by two.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E106-A No.12 pp.1504-1510

- Publication Date
- 2023/12/01

- Publicized
- 2023/08/24

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.2023SDP0005

- Type of Manuscript
- Special Section PAPER (Special Section on Signal Design and Its Applications in Communications)

- Category
- Digital Signal Processing

Ali ARDALANI

Otto von Guericke University Magdeburg

Alexander POTT

Otto von Guericke University Magdeburg

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Ali ARDALANI, Alexander POTT, "A New Transformation for Costas Arrays" in IEICE TRANSACTIONS on Fundamentals,
vol. E106-A, no. 12, pp. 1504-1510, December 2023, doi: 10.1587/transfun.2023SDP0005.

Abstract: A Costas array of size *n* is an *n* × *n* binary matrix such that no two of the $inom{n}{2}$ line segments connecting 1s have the same length and slope. Costas arrays are found by finite-field-based construction methods and their manipulations (systematically constructed) and exhaustive search methods. The arrays found exhaustively, which are of completely unknown origin, are called sporadic. Most studies in Costas arrays have tended to focus on systematically constructed Costas arrays rather than sporadic ones, which reveals the hardness of examining a link between systematically constructed Costas arrays and sporadic ones. This paper introduces a new transformation that preserves the Costas property for some Costas arrays, but not all. We observed that this transformation could transform some systematically constructed Costas arrays to sporadic ones and vice versa. Moreover, we introduce a family of arrays with the property that the auto-correlation of each array and the cross-correlation between any two arrays in this family is bounded above by two.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2023SDP0005/_p

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@ARTICLE{e106-a_12_1504,

author={Ali ARDALANI, Alexander POTT, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={A New Transformation for Costas Arrays},

year={2023},

volume={E106-A},

number={12},

pages={1504-1510},

abstract={A Costas array of size *n* is an *n* × *n* binary matrix such that no two of the $inom{n}{2}$ line segments connecting 1s have the same length and slope. Costas arrays are found by finite-field-based construction methods and their manipulations (systematically constructed) and exhaustive search methods. The arrays found exhaustively, which are of completely unknown origin, are called sporadic. Most studies in Costas arrays have tended to focus on systematically constructed Costas arrays rather than sporadic ones, which reveals the hardness of examining a link between systematically constructed Costas arrays and sporadic ones. This paper introduces a new transformation that preserves the Costas property for some Costas arrays, but not all. We observed that this transformation could transform some systematically constructed Costas arrays to sporadic ones and vice versa. Moreover, we introduce a family of arrays with the property that the auto-correlation of each array and the cross-correlation between any two arrays in this family is bounded above by two.},

keywords={},

doi={10.1587/transfun.2023SDP0005},

ISSN={1745-1337},

month={December},}

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TY - JOUR

TI - A New Transformation for Costas Arrays

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 1504

EP - 1510

AU - Ali ARDALANI

AU - Alexander POTT

PY - 2023

DO - 10.1587/transfun.2023SDP0005

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E106-A

IS - 12

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - December 2023

AB - A Costas array of size *n* is an *n* × *n* binary matrix such that no two of the $inom{n}{2}$ line segments connecting 1s have the same length and slope. Costas arrays are found by finite-field-based construction methods and their manipulations (systematically constructed) and exhaustive search methods. The arrays found exhaustively, which are of completely unknown origin, are called sporadic. Most studies in Costas arrays have tended to focus on systematically constructed Costas arrays rather than sporadic ones, which reveals the hardness of examining a link between systematically constructed Costas arrays and sporadic ones. This paper introduces a new transformation that preserves the Costas property for some Costas arrays, but not all. We observed that this transformation could transform some systematically constructed Costas arrays to sporadic ones and vice versa. Moreover, we introduce a family of arrays with the property that the auto-correlation of each array and the cross-correlation between any two arrays in this family is bounded above by two.

ER -