By Topic

Translation-invariant propelinear codes

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Rifa, J. ; Dept. d''Inf., Univ. Autonoma de Barcelona, Spain ; Pujol, J.

A class of binary group codes is investigated. These codes are the propelinear codes, defined over the Hamming metric space Fm, F=(0, 1), with a group structure. Generally, they are neither Abelian nor translation-invariant codes but they have good algebraic and combinatorial properties. Linear codes and Z4-linear codes can be seen as a subclass of propelinear codes. It is shown here that the subclass of translation-invariant propelinear codes is of type Z2k1⊕Z4k2⊕Q 8(k3) where Q8 is the non-Abelian quaternion group of eight elements. Exactly, every translation-invariant propelinear code of length n can be seen as a subgroup of Z2k1⊕Z4k2⊕Q 8k3 with k1+2k2+4k3 =n. For k2=k3=0 we obtain linear binary codes and for k1=k3=0 we obtain Z4-linear codes. The class of additive propelinear codes-the Abelian subclass of the translation-invariant propelinear codes-is studied and a family of nonlinear binary perfect codes with a very simply construction and a very simply decoding algorithm is presented

Published in:

Information Theory, IEEE Transactions on  (Volume:43 ,  Issue: 2 )