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TitleGr\"obner bases for the distance distribution of systematic codes.
Author(s) Eleonora Guerrini, Emmanuela Orsini, Ilaria Simonetti
TypeBook, Chapter in Book, Conference Proceeding
AbstractCoding theorists have been studying only linear codes, with a few exceptions (Preparata in Inform. Control 13(13):378400, 1968; Baker et al. in IEEE Trans. on Inf. Th. 29(3):342345, 1983). This is not surprising, since linear codes have a nice structure, easy to study and leading to efficient implementations. However, it is well-known that some non-linear codes have a higher distance (or a better distance distribution) that any linear code with the same parameters (Preparata in Inform. Control 13(13):378400, 1968; Pless et al. (eds.) in Handbook of Coding Theory, vols. I, II, North-Holland, Amsterdam, 1998). This translates into a superior decoding performance (Litsyn in Handbook of Coding Theory, vols. I, II, North-Holland, Amsterdam, pp. 463498, 1998).

Systematic non-linear codes are the most studied non-linear codes. We describe a Gröbner bases technique to compute the distance distribution for these codes.
ISBN978-3-540-93805-7/hbk; 978-3-5
URL http://link.springer.com/chapter/10.1007%2F978-3-540-93806-4_22
PublisherBerlin: Springer
Translation No
Refereed No