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## Refined analysis of RGHWs of code pairs coming from Garcia-Stichtenoth’s second tower

#### Olav GEİL [1] , Stefano MARTİN [2] , Umberto MARTÍNEZ-PEÑAS [3] , Diego RUANO [4]

Asymptotically good sequences of ramp secret sharing schemes were given in [5] by using one-point algebraic geometric codes defined from asymptotically good towers of function fields. Their security is given by the relative generalized Hamming weights of the corresponding codes. In this paper we demonstrate how to obtain refined information on the RGHWs when the codimension of the codes is small. For general codimension, we give an improved estimate for the highest RGHW.
Algebraic geometric codes, Asymptotically good ramp secret sharing schemes, Generalized Hamming weights, Relative generalized Hamming weights, Secret sharing
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Subjects Engineering Articles Author: Olav GEİL Author: Stefano MARTİN Author: Umberto MARTÍNEZ-PEÑAS Author: Diego RUANO Publication Date : January 11, 2017
 Bibtex @research article { jacodesmath284557, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, eissn = {2148-838X}, address = {}, publisher = {Yildiz Technical University}, year = {2017}, volume = {4}, pages = {37 - 47}, doi = {10.13069/jacodesmath.34390}, title = {Refined analysis of RGHWs of code pairs coming from Garcia-Stichtenoth’s second tower}, key = {cite}, author = {Gei̇l, Olav and Marti̇n, Stefano and Martínez-peñas, Umberto and Ruano, Diego} } APA Gei̇l, O , Marti̇n, S , Martínez-peñas, U , Ruano, D . (2017). Refined analysis of RGHWs of code pairs coming from Garcia-Stichtenoth’s second tower . Journal of Algebra Combinatorics Discrete Structures and Applications , 4 (1) , 37-47 . DOI: 10.13069/jacodesmath.34390 MLA Gei̇l, O , Marti̇n, S , Martínez-peñas, U , Ruano, D . "Refined analysis of RGHWs of code pairs coming from Garcia-Stichtenoth’s second tower" . Journal of Algebra Combinatorics Discrete Structures and Applications 4 (2017 ): 37-47 Chicago Gei̇l, O , Marti̇n, S , Martínez-peñas, U , Ruano, D . "Refined analysis of RGHWs of code pairs coming from Garcia-Stichtenoth’s second tower". Journal of Algebra Combinatorics Discrete Structures and Applications 4 (2017 ): 37-47 RIS TY - JOUR T1 - Refined analysis of RGHWs of code pairs coming from Garcia-Stichtenoth’s second tower AU - Olav Gei̇l , Stefano Marti̇n , Umberto Martínez-peñas , Diego Ruano Y1 - 2017 PY - 2017 N1 - doi: 10.13069/jacodesmath.34390 DO - 10.13069/jacodesmath.34390 T2 - Journal of Algebra Combinatorics Discrete Structures and Applications JF - Journal JO - JOR SP - 37 EP - 47 VL - 4 IS - 1 SN - -2148-838X M3 - doi: 10.13069/jacodesmath.34390 UR - https://doi.org/10.13069/jacodesmath.34390 Y2 - 2020 ER - EndNote %0 Journal of Algebra Combinatorics Discrete Structures and Applications Refined analysis of RGHWs of code pairs coming from Garcia-Stichtenoth’s second tower %A Olav Gei̇l , Stefano Marti̇n , Umberto Martínez-peñas , Diego Ruano %T Refined analysis of RGHWs of code pairs coming from Garcia-Stichtenoth’s second tower %D 2017 %J Journal of Algebra Combinatorics Discrete Structures and Applications %P -2148-838X %V 4 %N 1 %R doi: 10.13069/jacodesmath.34390 %U 10.13069/jacodesmath.34390 ISNAD Gei̇l, Olav , Marti̇n, Stefano , Martínez-peñas, Umberto , Ruano, Diego . "Refined analysis of RGHWs of code pairs coming from Garcia-Stichtenoth’s second tower". Journal of Algebra Combinatorics Discrete Structures and Applications 4 / 1 (January 2017): 37-47 . https://doi.org/10.13069/jacodesmath.34390 AMA Gei̇l O , Marti̇n S , Martínez-peñas U , Ruano D . Refined analysis of RGHWs of code pairs coming from Garcia-Stichtenoth’s second tower. Journal of Algebra Combinatorics Discrete Structures and Applications. 2017; 4(1): 37-47. Vancouver Gei̇l O , Marti̇n S , Martínez-peñas U , Ruano D . Refined analysis of RGHWs of code pairs coming from Garcia-Stichtenoth’s second tower. Journal of Algebra Combinatorics Discrete Structures and Applications. 2017; 4(1): 37-47.

##### Relative generalized Hamming weights of $q$-ary Reed-Muller codes
###### https://doi.org/10.3934/amc.2017041
Authors of the Article
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