FEW-WEIGHT CODES FROM TRACE CODES OVER

2018 ◽  
Vol 98 (1) ◽  
pp. 167-174
Author(s):  
MINJIA SHI ◽  
YUE GUAN ◽  
CHENCHEN WANG ◽  
PATRICK SOLÉ
Keyword(s):  
Secret Sharing ◽  
Infinite Family ◽  
Gray Map ◽  
Secret Sharing Schemes ◽  
Lee Weight ◽  
Trace Codes ◽  
Defining Sets

We construct two families of few-weight codes for the Lee weight over the ring $R_{k}$ based on two different defining sets. For the first defining set, taking the Gray map, we obtain an infinite family of binary two-weight codes which are in fact $2^{k}$-fold replicated MacDonald codes. For the second defining set, we obtain two infinite families of few-weight codes. These few-weight codes can be used to implement secret-sharing schemes.

scholarly journals Five-weight codes from three-valued correlation of M-sequences

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Minjia Shi ◽  
Liqin Qian ◽  
Tor Helleseth ◽  
Patrick Solé
Keyword(s):  
Algebraic Structure ◽  
Secret Sharing ◽  
Weight Distribution ◽  
Infinite Family ◽  
Character Sums ◽  
Secret Sharing Schemes ◽  
Trace Codes ◽  
Sequence Correlation ◽  
Abelian Codes ◽  
M Sequences

<p style='text-indent:20px;'>In this paper, for each of six families of three-valued <inline-formula><tex-math id="M1">\begin{document}$ m $\end{document}</tex-math></inline-formula>-sequence correlation, we construct an infinite family of five-weight codes from trace codes over the ring <inline-formula><tex-math id="M2">\begin{document}$ R = \mathbb{F}_2+u\mathbb{F}_2 $\end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id="M3">\begin{document}$ u^2 = 0. $\end{document}</tex-math></inline-formula> The trace codes have the algebraic structure of abelian codes. Their Lee weight distribution is computed by using character sums. Their support structure is determined. An application to secret sharing schemes is given. The parameters of the binary image are <inline-formula><tex-math id="M4">\begin{document}$ [2^{m+1}(2^m-1),4m,2^{m}(2^m-2^r)] $\end{document}</tex-math></inline-formula> for some explicit <inline-formula><tex-math id="M5">\begin{document}$ r. $\end{document}</tex-math></inline-formula></p>

scholarly journals A Flaw in the Use of Minimal Defining Sets for Secret Sharing Schemes

2006 ◽  
Vol 40 (2) ◽  
pp. 225-236 ◽  
Author(s):  
Mike J. Grannell ◽  
Terry S. Griggs ◽  
Anne Penfold Street
Keyword(s):  
Secret Sharing ◽  
Secret Sharing Schemes ◽  
Defining Sets

scholarly journals Two-weight and three-weight linear codes constructed from Weil sums

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Tonghui Zhang ◽  
Hong Lu ◽  
Shudi Yang
Keyword(s):  
Secret Sharing ◽  
Linear Codes ◽  
Association Schemes ◽  
Strongly Regular Graphs ◽  
Secret Sharing Schemes ◽  
Regular Graphs ◽  
Authentication Codes ◽  
Strongly Regular ◽  
Weil Sums ◽  
Defining Sets

<p style='text-indent:20px;'>Linear codes with few weights are widely used in strongly regular graphs, secret sharing schemes, association schemes and authentication codes. In this paper, we construct several two-weight and three-weight linear codes over finite fields by choosing suitable different defining sets. We also give some examples and some of the codes are optimal or almost optimal. Their applications to secret sharing schemes are also investigated.</p>

A Strengthened Security Notion for Password-Protected Secret Sharing Schemes

2015 ◽  
Vol E98.A (1) ◽  
pp. 203-212 ◽  
Author(s):  
Shingo HASEGAWA ◽  
Shuji ISOBE ◽  
Jun-ya IWAZAKI ◽  
Eisuke KOIZUMI ◽  
Hiroki SHIZUYA
Keyword(s):  
Secret Sharing ◽  
Secret Sharing Schemes ◽  
Security Notion

scholarly journals On the classification of ideal secret sharing schemes

1991 ◽  
Vol 4 (2) ◽  
pp. 123-134 ◽  
Author(s):  
Ernest F. Brickell ◽  
Daniel M. Davenport
Keyword(s):  
Secret Sharing ◽  
Secret Sharing Schemes ◽  
Ideal Secret Sharing Schemes

Geometric secret sharing schemes and their duals

1994 ◽  
Vol 4 (1) ◽  
pp. 83-95 ◽  
Author(s):  
Wen-Ai Jackson ◽  
Keith M. Martin
Keyword(s):  
Secret Sharing ◽  
Secret Sharing Schemes

scholarly journals Fully Dynamic Secret Sharing Schemes

1994 ◽  
pp. 110-125 ◽  
Author(s):  
C. Blundo ◽  
A. Cresti ◽  
A. De Santis ◽  
U. Vaccaro
Keyword(s):  
Secret Sharing ◽  
Secret Sharing Schemes
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