清醒 发表于 2025-3-23 13:19:02

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 发表于 2025-3-23 15:15:22

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易于 发表于 2025-3-23 18:31:33

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商议 发表于 2025-3-24 01:48:56

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).

勤劳 发表于 2025-3-24 04:59:43

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dilute 发表于 2025-3-24 10:16:00

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Adj异类的 发表于 2025-3-24 10:46:59

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寒冷 发表于 2025-3-24 17:31:45

1431-1550theorem 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

关心 发表于 2025-3-24 21:00:50

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reaching 发表于 2025-3-25 01:23:35

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).
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查看完整版本: 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