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- W1603089898 abstract "Publisher SummaryA linear code C is self-dual if C = C⊥. Many good codes are self-dual, among them are the extended Golay codes and certain quadratic residue codes. The most important property of self-dual codes is given by Gleason's theorem, which imposes strong constraints on the weight enumerator. This theorem is proved by a powerful nineteenth-century technique known as invariant theory. The same technique proves numerous similar theorems, dealing with other kinds of weight enumerators. Most of the results in this chapter apply equally well to a larger class of codes—namely, linear or nonlinear codes with the property that the transform of the distance distribution is equal to the distance distribution (for example, the Nordstrom–Robinson code). Such codes are called fomally “self -dual.” The formally self-dual codes encountered in this chapter have the same distance distribution as weight distribution, and so it works throughout with the weight distribution." @default.
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- W1603089898 date "1977-01-01" @default.
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- W1603089898 title "19 Self-dual codes and invariant theory" @default.
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