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In coding theory, a constant-weight code, also called an m of n code, is an error detection and correction code where all codewords share the same Hamming weight. The one-hot code and the balanced code are two widely-used kinds of constant-weight code. The theory is closely connected to that of designs (such as ''t''-designs and Steiner systems). Most of the work on this very vital field of discrete mathematics is concerned with ''binary'' constant-weight codes. Binary constant-weight codes have several applications, including frequency hopping in GSM networks.〔D. H. Smith, L. A. Hughes and S. Perkins (2006). "(A New Table of Constant Weight Codes of Length Greater than 28 )". ''The Electronic Journal of Combinatorics'' 13.〕 Most barcodes use a binary constant-weight code to simplify automatically setting the threshold. Most line codes use either a constant-weight code, or a nearly-constant-weight paired disparity code. In addition to use as error correction codes, the large space between code words can also be used in the design of asynchronous circuits such as delay insensitive circuits. Constant-weight codes, like Berger codes, can detect all unidirectional errors. == ''A''(''n'',''d'',''w'') == The central problem regarding constant-weight codes is the following: what is the maximum number of codewords in a binary constant-weight code with length , Hamming distance , and weight ? This number is called . Apart from some trivial observations, it is generally impossible to compute these numbers in a straightforward way. Upper bounds are given by several important theorems such as the ''first and second Johnson bounds'',〔See pp. 526–527 of F. J. MacWilliams and N. J. A. Sloane (1979). ''The Theory of Error-Correcting Codes''. Amsterdam: North-Holland.〕 and better upper bounds can sometimes be found in other ways. Lower bounds are most often found by exhibiting specific codes, either with use of a variety of methods from discrete mathematics, or through heavy computer searching. A large table of such record-breaking codes was published in 1990,〔A. E. Brouwer, James B. Shearer, N. J. A. Sloane and Warren D. Smith (1990). "A New Table of Constant Weight Codes". ''IEEE Transactions of Information Theory'' 36.〕 and an extension to longer codes (but only for those values of and which are relevant for the GSM application) was published in 2006.〔 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「Constant-weight code」の詳細全文を読む スポンサード リンク
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