關(guān)于Goppa碼的維數(shù)問題
ON THE DIMENSIONS OF GOPPA CODES
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摘要: 馮貴良(1983)給出了Coppa碼維數(shù)的新下限。本文首先給出了在一定條件下求這一下限的統(tǒng)一公式。然后給出了Goppa碼維數(shù)上限以及求這一上限的具體方法。通過上、下限同時估計,能夠求出特殊類型的Goppa碼的維數(shù)。
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關(guān)鍵詞:
- Goppa碼; Goppa碼的維數(shù); 維數(shù)的限
Abstract: A new lower bound on the dimensions of Goppa codes bas been given by Feng Guiliang (1983). In this paper, at first, a formula for computing the lower bound in some cases is offered, and a upper bound on the dimensions of Goppa codes and a method of finding the upper bound are given. In some special cases, the dimensions of Goppa codes can be obtained by using the upper bound and the lower bound. -
V. D. Goppa, Probl. Peredach. Inform., 6(1970)3, 24-30.[2]E.R.BerIekamp, IEEE Trans. on IT, IT-19(1973)9, 590-592.[3]F.J.Macwillians, N.J.A. Sloane, Theory of Error-Correcting Codes, New York, North-Holland, (1977).[4]馮貴良,電子學(xué)報,1983年,第2期,第66-72頁.[5]K.K.Tzeng,E.Iimmermann, IEEE.Trans. on IT, IT-21(1975)11, 712-716.[6]岳殿武,循環(huán)陪集結(jié)構(gòu)及其應(yīng)用,系統(tǒng)科學(xué)與數(shù)學(xué),待發(fā)表. -
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