Acta mathematica scientia,Series A ›› 1999, Vol. 19 ›› Issue (4): 368-372.
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Abstract:
By using the dual distance distribution and its properties for binary code C with length n and number of codewords M, the Althofer-Sillke inequality is improved when M is odd. The exact values of minimum average Hamming distance of C are determined when M equals 2n-1 or 2n-1-1.
Key words: Ｈａｍｍｉｎｇｄｉｓｔａｎｃｅ, Ｄｕａｌｄｉｓｔａｎｃｅｄｉｓｔｒｉｂｕｔｉｏｎ, Ａｌｔｈ¨ｏｆｅｒＳｉｌｌｋｅｉｎｅｑｕａｌｉｔｙ
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Xia Shutao Fu Fangwei. On the average hamming distance and variance for binary codes[J].Acta mathematica scientia,Series A, 1999, 19(4): 368-372.
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http://121.43.60.238/sxwlxbA/EN/Y1999/V19/I4/368
１ Ａｌｔｈ¨ｏｆｅｒＩ，ＳｉｌｌｋｅＴ．ＡｎＡｖｅｒａｇｅＤｉｓｔａｎｃｅＩｎｅｑｕａｌｉｔｙｆｏｒＬａｒｇｅＳｕｂｓｅｔｓｏｆｔｈｅＣｕｂｅ．ＪｏｕｒｎａｌｏｆＣｏｍｂｉｎａｔｏｒｉａｌＴｈｅｏｒｙ，ＳｅｒｉｅｓＢ，１９９２，５６：２９６－３０１ ２ ＦｕＦａｎｇｗｅｉ，ＳｈｅｎＳｈｉｙｉ．ＯｎｔｈｅｅｘｐｅｃｔａｔｉｏｎａｎｄｖａｒｉａｎｃｅｏｆＨａｍｍｉｎｇｄｉｓｔａｎｃｅｂｅｔｗｅｅｎｔｗｏｉ．ｉ．ｄ．ｒａｎｄｏｍｖｅｃｔｏｒｓ．ＡｃｔａＭａｔｈｅｍａｔｉｃａｅＡｐｐｌｉｃａｔｅＳｉｎｉｃａ，１９９７，１３：２４３－２５０ ３ ＡｈｌｓｗｅｄｅＲ，ＫａｔｏｎａＧ．ＣｏｎｔｒｉｂｕｔｉｏｎｓｔｏｔｈｅｇｅｏｍｅｔｒｙｏｆＨａｍｍｉｎｇｓｐａｃｅｓ．ＤｉｓｃｒｅｔｅＭａｔｈ，１９７７，１７：１－２２ ４ ＡｈｌｓｗｅｄｅＲ，Ａｌｔｈ¨ｏｆｅｒＩ．Ｔｈｅａｓｙｍｐｔｏｔｉｃｂｅｈａｖｉｏｕｒｏｆｄｉａｍｅｔｅｒｓｉｎｔｈｅａｖｅｒａｇｅ．ＪｏｕｒｎａｌｏｆＣｏｍｂｉｎａｔｏｒｉａｌＴｈｅｏｒｙ，ＳｅｒｉｅｓＢ，１９９４，６１：１６７－１７７ ５ 符方伟．关于编码理论中Ｐｌｏｔｋｉｎ界和ＧｒｅｙＲａｎｋｉｎ界的几个注记．南开大学学报（自然科学），１９９４，１２（４） ６ ＭａｃＷｉｌｌｉａｍｓＦＪ，ＳｌｏａｎＮＪＡ．ＴｈｅＴｈｅｏｒｙｏｆＥｒｒｏｒｃｏｒｒｅｃｔｉｎｇＣｏｄｅｓ．Ｎｅｗ Ｙｏｒｋ：ＮｏｒｔｈＨｏｌｌａｎｄ，１９７７
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