Details:
Title  Gr\"obner bases for the distance distribution of systematic codes.  Author(s)  Eleonora Guerrini, Emmanuela Orsini, Ilaria Simonetti  Type  Book, Chapter in Book, Conference Proceeding  Abstract  Coding theorists have been studying only linear codes, with a few exceptions (Preparata in Inform. Control 13(13):378–400, 1968; Baker et al. in IEEE Trans. on Inf. Th. 29(3):342–345, 1983). This is not surprising, since linear codes have a nice structure, easy to study and leading to efficient implementations. However, it is wellknown that some nonlinear codes have a higher distance (or a better distance distribution) that any linear code with the same parameters (Preparata in Inform. Control 13(13):378–400, 1968; Pless et al. (eds.) in Handbook of Coding Theory, vols. I, II, NorthHolland, Amsterdam, 1998). This translates into a superior decoding performance (Litsyn in Handbook of Coding Theory, vols. I, II, NorthHolland, Amsterdam, pp. 463–498, 1998).
Systematic nonlinear codes are the most studied nonlinear codes. We describe a Gröbner bases technique to compute the distance distribution for these codes.  ISBN  9783540938057/hbk; 97835 
URL 
http://link.springer.com/chapter/10.1007%2F9783540938064_22 
Language  English  Pages  367372  Publisher  Berlin: Springer  Year  2009  Edition  0  Translation 
No  Refereed 
No 
