The perfect binary one-error-correcting codes of length 15: part II-properties
IEEE Transactions on Information Theory（2010）
摘要
A complete classification of the perfect binary one-error-correcting codes of length 15, as well as their extensions of length 16, was recently carried out in [P. R. J. Östergård and O. Pottonen, "The perfect binary one-error-correcting codes of length 15: Part I--Classification," IEEE Trans. Inf. Theory vol. 55, pp. 4657-4660, 2009]. In the current accompanying work, the classified codes are studied in great detail, and their main properties are tabulated. The results include the fact that 33 of the 80 Steiner triple systems of order 15 occur in such codes. Further understanding is gained on full-rank codes via switching, as it turns out that all but two full-rank codes can be obtained through a series of such transformations from the Hamming code. Other topics studied include (non)systematic codes, embedded one-error-correcting codes, and defining sets of codes. A classification of certain mixed perfect codes is also obtained.
更多查看译文
关键词
complete classification,embedded one-error-correcting code,i-component,index terms— classification,certain mixed perfect code,steiner triple system,perfect binary,full-rank code,p. r,steiner system,per- fect code,classified code,ieee trans,hamming code,part ii-properties,hamming codes,galois fields,classification,kernel,mathematics,statistics,switches,information theory,binary codes,automation,systematic code,switching,error correction code
AI 理解论文
溯源树
样例
生成溯源树，研究论文发展脉络
Chat Paper
正在生成论文摘要