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Lexicographic codes or lexicodes are greedily generated error-correcting codes with remarkably good properties. They were produced independently by Levenshtein〔V.I. Levenstein. A class of systematic codes. Soviet Math. Dokl, 1(1):368-371, 1960.〕 and Conway and Sloane 〔J.H. Conway and N.J.A Sloane. Lexicographic codes: error-correcting codes from game theory. IEEE Transactions on Information Theory, 32:337-348, 1986.〕 and are known to be linear over some finite fields. == Construction == A lexicode of minimum distance ''d'' and length ''n'' over a finite field is generated by starting with the all-zero vector and iteratively adding the next vector (in lexicographic order) of minimum Hamming distance ''d'' from the vectors added so far. As an example, the length-3 lexicode of minimum distance 2 would consist of the vectors marked by an "X" in the following example: : Since lexicodes are linear, they can also be constructed by means of their basis. 〔Ari Trachtenberg, Designing Lexicographic Codes with a Given Trellis Complexity, IEEE Transactions on Information Theory, January 2002.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Lexicographic code」の詳細全文を読む スポンサード リンク
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