54 research outputs found
A Note on the Injection Distance
Koetter and Kschischang showed in [R. Koetter and F.R. Kschischang, "Coding
for Errors and Erasures in Random Network Coding," IEEE Trans. Inform. Theory,
{54(8), 2008] that the network coding counterpart of Gabidulin codes performs
asymptotically optimal with respect to the subspace distance. Recently, Silva
and Kschischang introduced in [D. Silva and F.R. Kschischang, "On Metrics for
Error Correction in Network Coding," To appear in IEEE Trans. Inform. Theory,
ArXiv: 0805.3824v4[cs.IT], 2009] the injection distance to give a detailed
picture of what happens in noncoherent network coding. We show that the above
codes are also asymptotically optimal with respect to this distance
New Parameters of Linear Codes Expressing Security Performance of Universal Secure Network Coding
The universal secure network coding presented by Silva et al. realizes secure
and reliable transmission of a secret message over any underlying network code,
by using maximum rank distance codes. Inspired by their result, this paper
considers the secure network coding based on arbitrary linear codes, and
investigates its security performance and error correction capability that are
guaranteed independently of the underlying network code. The security
performance and error correction capability are said to be universal when they
are independent of underlying network codes. This paper introduces new code
parameters, the relative dimension/intersection profile (RDIP) and the relative
generalized rank weight (RGRW) of linear codes. We reveal that the universal
security performance and universal error correction capability of secure
network coding are expressed in terms of the RDIP and RGRW of linear codes. The
security and error correction of existing schemes are also analyzed as
applications of the RDIP and RGRW.Comment: IEEEtran.cls, 8 pages, no figure. To appear in Proc. 50th Annual
Allerton Conference on Communication, Control, and Computing (Allerton 2012).
Version 2 added an exact expression of the universal error correction
capability in terms of the relative generalized rank weigh
Optimal Ferrers Diagram Rank-Metric Codes
Optimal rank-metric codes in Ferrers diagrams are considered. Such codes
consist of matrices having zeros at certain fixed positions and can be used to
construct good codes in the projective space. Four techniques and constructions
of Ferrers diagram rank-metric codes are presented, each providing optimal
codes for different diagrams and parameters.Comment: to be presented in Algebra, Codes, and Networks, Bordeaux, June 16 -
20, 201
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