The Perfect Binary One-Error-Correcting Codes of Length 15: Part II-Properties

被引：23
作者：
Ostergard, Patric R. J. [1 ]
Pottonen, Olli [1 ]
Phelps, Kevin T. [2 ]
机构：
[1] Aalto Univ, Dept Commun & Networking, Aalto 00076, Finland
[2] Auburn Univ, Dept Math & Stat, Auburn, AL 36849 USA
来源：
IEEE TRANSACTIONS ON INFORMATION THEORY | 2010年 / 56卷 / 06期
基金：
芬兰科学院;
关键词：
Classification; Hamming code; perfect code; Steiner system; switching; STEINER TRIPLE-SYSTEMS; ORTHOGONAL ARRAYS; TILINGS; GRAPHS; SPACES;
D O I：
10.1109/TIT.2010.2046197
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
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. Ostergard 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.
引用
收藏
页码：2571 / 2582
页数：12
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