Research PaperNo Access

Classification of a class of $A^{3} MDS$ $A^{3} MDS$ code and applications in secret-sharing schemes

Bandana Pandey

https://orcid.org/0000-0002-3195-8807

Department of Mathematics, BITS-Pilani, Goa campus, NH-17B, Zuarinagar, Goa 403726, India

E-mail Address: pandeybandana10@gmail.com

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and

Prabal Paul

https://orcid.org/0000-0002-3483-835X

Department of Mathematics, BITS-Pilani, Goa campus, NH-17B, Zuarinagar, Goa 403726, India

E-mail Address: prabal.paul@gmail.com

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https://doi.org/10.1142/S1793830923500842Cited by:1 (Source: Crossref)

Abstract

A $q$ $q$ -ary linear $[n, k, n - k - (i - 1)]$ $[n, k, n - k - (i - 1)]$ code $ℒ$ is known as $A^{i} MDS$ code. If $d = n - k + 1,$ the code is called a maximum distance separable code. $MDS$ codes are known to be useful in the secret-sharing schemes and coding theory. In this paper, we classify all binary self-orthogonal $A^{3} MDS$ codes. We have introduced a subclass of $A^{3} MDS$ codes, called $N^{3} STMDS$ codes, to form a special type of secret-sharing scheme where for any participant, there exist $(k - 1)$ other participants who can collectively reveal the secret by combining their shares and there exists another set of $(k + 2)$ participants including the given participant, who cannot reveal the secret.

Keywords:

AMSC: 94B05, 94A60, 94A62

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