Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE International Symposium on Information Theory (ISIT)

The simplex codes are not optimal for binary symmetric channels

Tor Helleseth, Torleiv Kløve, V.I. Levenshtein

Published Jan 1, 2003• 0 citations
Publisher

Abstract

It is shown that the [2/sup K/-1,k] simplex codes are not optimal for error correction on the binary symmetric channel with bit error probability p, where 0<p<;1/2 (for k/spl ges/3).
DOI
10.1109/isit.2003.1228175

Related papers

A coset weight count that proves that the simplex codes are not optimal for error correction

Tor Helleseth, Torleiv Kløve, V.I. Levenshtein

The number of cosets of weight 2/sup k-2/ or less are determined for the [2/sup k/-1, k, 2/sup k-1/] simplex code and a [2/sup k/-1, k, 2/sup k-1/-1] code obtained by a simple modification of the simplex code. The result proves that the [2/sup k/-1, k] simplex codes are not optimal for error correction on the binary symmetric channel with small bit error probability, p, (for k/spl ges/3). A proof that the modified code is better for all p, 0<p<1/2, is sketched.

IEEE Information Theory Workshop (ITW)•Mar 1, 2004•2 citations

The Simplex Codes and Other Even-Weight Binary Linear Codes for Error Correction

Tor Helleseth, Torleiv Kløve, V.I. Levenshtein

The probability of correct decoding on the binary-symmetric channel is studied. In particular, a class of codes with the same lengths and dimensions as the linear simplex codes, but with larger probability of correct decoding for all parameters p, 0 < p < 1/2, is given.

IEEE Transactions on Information Theory•Oct 26, 2004•7 citations

On the probability of undetected error for binary codes used for combined correction and detection

Iiro S. Honkala, Tero K Laihonen

We show that for a code used for combined error correction and detection in the binary symmetric channel, the probability of an undetected error can have several local maxima.

Journal of Discrete Mathematical Sciences and Cryptography•Aug 1, 2001•2 citations

Necessary conditions for good error detection

P.N. Perry

The problem of determining the error detection capabilities of linear codes where the channel is a binary symmetric channel is addressed. Necessary conditions are given on the number of codewords in an (n,k) linear code and its dual for the probability of an undetected error to be upper bounded by 2/sup -(n-k)/.>

IEEE Transactions on Information Theory•Mar 1, 1991•17 citations

Bounds on the undetected error probabilities of linear codes for both error correction and detection

Mao‐Chao Lin

The author investigates the (n, k, d>or=2t+1) binary linear codes, which are used for correcting error patterns of weight at most t and detecting other error patterns over a binary symmetric channel. In particular, for t=1, it is shown that there exists one code whose probability of undetected errors is upper-bounded by (n+1) (2/sup n-k/-n)/sup -1/ when used on a binary symmetric channel with transition probability less than 2/n.>

IEEE Transactions on Information Theory•Jan 1, 1990•0 citations

Methods for Calculating Exact Bit Error Probability of a Binary Linear Code over Binary Symmetric Channel

Tadashi Wadayama

IEEE International Symposium on Information Theory (ISIT)•Dec 4, 2001•0 citations