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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Generalized Column Distances

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Author(s):
Cardell, Sara D. [1] ; Firer, Marcelo [1] ; Napp, Diego [2]
Total Authors: 3
Affiliation:
[1] Univ Estadual Campinas, Imecc, BR-13083970 Campinas - Brazil
[2] Univ Alicante, Dept Math, Alicante 03690 - Spain
Total Affiliations: 2
Document type: Journal article
Source: IEEE TRANSACTIONS ON INFORMATION THEORY; v. 66, n. 11, p. 6863-6871, NOV 2020.
Web of Science Citations: 0
Abstract

The notion of Generalized Hamming weights of block codes has been investigated since the nineties due to its significant role in coding theory and cryptography. In this paper we extend this concept to the context of convolutional codes. In particular, we focus on column distances and introduce the novel notion of generalized column distances (GCD). We first show that the hierarchy of GCD is strictly increasing. We then provide characterizations of such distances in terms of the truncated parity-check matrix of the code, that will allow us to determine their values. Finally, the case in which the parity-check matrix is in systematic form is treated. (AU)

FAPESP's process: 15/07246-0 - Construction, decoding and implementation of F_q linear codes. Performanca of SPC product codes and cryptanalysis of the shrinking generators.
Grantee:Sara Díaz Cardell
Support Opportunities: Scholarships in Brazil - Post-Doctoral
FAPESP's process: 13/25977-7 - Security and reliability of Information: theory and practice
Grantee:Marcelo Firer
Support Opportunities: Research Projects - Thematic Grants