Titlebook: Self-Dual Codes and Invariant Theory; Gabriele Nebe,Eric M. Rains,Neil J.A. Sloane Book 2006 Springer-Verlag Berlin Heidelberg 2006 Code.E

清醒

Further Examples of Self-Dual Codes,This chapter describes some families of self-dual codes that cannot be obtained from representations of quasisimple form rings: codes over Z/mZ (§8.1), then the special cases of codes over Z/4Z (§8.2) and Z/8Z (§8.3), codes over more general Galois rings (§8.4), and codes over F. + F. . with . = 0 (§8.5).

手段

易于

商議

The Main Theorems,d in §5.5. They show that under quite general conditions, the invariant ring of the Clifford-Weil group .(.) associated with a finite representation . of a form ring is spanned by the complete weight enumerators of self-dual isotropic codes of Type . (and arbitrary length).

勤勞

dilute

Adj異類的

寒冷

1431-1550 theorem about the weight enumerators of self-dual codes and their connections with invariant theory. In the past 35 years there have been hundreds of papers written about generalizations and applications of this theorem to different types of codes. This self-contained book develops a new theory whi

關(guān)心

reaching

The Category Quad,and in the proofs of the main theorems in Chapter 5. Another application will be the definition of the Witt group of representations of a form ring (§4.6). This will be used to define the universal Clifford-Weil group associated with a finite form ring (see §5.4).