New Soft Set Based Class of Linear Algebraic Codes
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Department of Mathematics, Environment and Science, University of Southern Queensland, Springfield, QLD 4300, Australia
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Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan
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Division of Data Science, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam
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Faculty of Information Technology, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam
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Department of Mathematics and Sciences, University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA
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School of Computer Science and Engineering, VIT, Vellore, Tamil Nadu 632014, India
*
Author to whom correspondence should be addressed.
Symmetry 2018, 10(10), 510; https://doi.org/10.3390/sym10100510
Received: 17 September 2018 / Revised: 12 October 2018 / Accepted: 15 October 2018 / Published: 16 October 2018
In this paper, we design and develop a new class of linear algebraic codes defined as soft linear algebraic codes using soft sets. The advantage of using these codes is that they have the ability to transmit m-distinct messages to m-set of receivers simultaneously. The methods of generating and decoding these new classes of soft linear algebraic codes have been developed. The notion of soft canonical generator matrix, soft canonical parity check matrix, and soft syndrome are defined to aid in construction and decoding of these codes. Error detection and correction of these codes are developed and illustrated by an example.
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Keywords:
linear algebraic code; soft set theory; soft linear algebraic code; soft communication; soft syndrome; soft codewords; soft generator matrix
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MDPI and ACS Style
Ali, M.; Khan, H.; Son, L.H.; Smarandache, F.; Kandasamy, W.B.V. New Soft Set Based Class of Linear Algebraic Codes. Symmetry 2018, 10, 510. https://doi.org/10.3390/sym10100510
AMA Style
Ali M, Khan H, Son LH, Smarandache F, Kandasamy WBV. New Soft Set Based Class of Linear Algebraic Codes. Symmetry. 2018; 10(10):510. https://doi.org/10.3390/sym10100510
Chicago/Turabian StyleAli, Mumtaz; Khan, Huma; Son, Le H.; Smarandache, Florentin; Kandasamy, W. B.V. 2018. "New Soft Set Based Class of Linear Algebraic Codes" Symmetry 10, no. 10: 510. https://doi.org/10.3390/sym10100510
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