Open AccessProceedings Article
Antichain codes
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It is shown that almost all codes satisfy an antichain condition, which states that the minimum length of a two dimensional subcode of a code C increases if the subcode is constrained to contain a minimum weight codeword.Abstract:
We show that almost all codes satisfy an antichain condition. This states that the minimum length of a two dimensional subcode of C increases if the subcode is constrained to contain a minimum weight codeword. In particular, almost no code satisfies the chain condition.read more
Citations
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Journal ArticleDOI
Some new characters on the wire-tap channel of type II
TL;DR: The generalized Hamming weight of Wei and the dimension/length profile (DLP) of Forney are extended to two-code formats and are useful to design a perfect secrecy coding scheme for the coordinated multiparty model.
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On the second greedy weight for linear codes of dimension 3
Wende Chen,Torleiv Kløve +1 more
TL;DR: It is shown that the problem is essentially equivalent to finding certain weighting of the points in the projective plane, and weighting which give the maximal value of g 2 − d 2 are determined in almost all cases.
Journal ArticleDOI
On the Weight Hierarchy of Product Codes
TL;DR: This paper generalizes the formula for the generalized Hamming weights of V ⊗ W in terms of those of V and W to a product code with more than two components.
Book ChapterDOI
On the Second Greedy Weight for Binary Linear Codes
Wende Chen,Torleiv Kløve +1 more
TL;DR: The difference g2 - d2 for a binary linear [n, k, d] code C is studied and upper and lower bounds on the maximal value are given.
Journal ArticleDOI
On the second greedy weight for linear codes of dimension at least 4
Wende Chen,Torleiv Kløve +1 more
TL;DR: Upper and lower bounds on the maximum of g/ sub 2/-d/sub 2/ for linear [n,k,d;q] codes C are given.
References
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Book
The Theory of Error-Correcting Codes
TL;DR: This book presents an introduction to BCH Codes and Finite Fields, and methods for Combining Codes, and discusses self-dual Codes and Invariant Theory, as well as nonlinear Codes, Hadamard Matrices, Designs and the Golay Code.
Book
Designs and their codes
TL;DR: The standard geometric codes are presented, followed by a list of recommended designs and some examples of how these designs might be implemented in the real world.
Book ChapterDOI
Wire-tap channel II
TL;DR: The optimal trade-offs among the parameters K, N, and μ and the intruder's uncertainty H (H is the "conditional entropy" of the data given the μ intercepted channel bits) were found and a system exists with H ≈ K − l.
Journal ArticleDOI
Polynomial weights and code constructions
TL;DR: It is shown that the polynomials (x - c)^i, i = 0,1,2,\cdots, have the "weight-retaining" property that any linear combination of these polynmials with coefficients in GF(q) has Hamming weight at least as great as that of the minimum degree polynomial included.