Generalized Hamming Weights for Linear Codes

By I. G. Núñez, Alicia Urdapilleta. 2001

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Applications of LDPC Codes to the Wiretap Channel (2004, background): “It was further shown in [4] that if I ( X ; Y ) and I ( X ; Z ) are individually maximized by the same P X ( x ) , and the main channel ( X → Y ) is less noisy than the wire tap channel ( X → Z ), then where Capacity(.) refers to the usual channel capacity.”
Higher Weights of Grassmann Codes (2000, background): “[15]) that the higher weights of any linear code satisfy the Griesmer-Wei bound:”
Wireless Information-Theoretic Security (2008, background): “Much of previous work for the wiretap channel stems from the early work in [2] and [16] and is studied more extensively by Wei [17], who shows how to encode secret information using cosets of certain linear block codes.”
Achieving the Secrecy Capacity of Wiretap Channels Using Polar Codes (2010, methodology): “Provably optimal coding schemes for this case can be constructed from MDS codes [40], or using extractors [7].”
Extrinsic information transfer functions: model and erasure channel properties (2004, background): “the latter are refinements of the weight enumerators of a code [33]–[35].”