The Perfect Binary One-Error-Correcting Codes of Length 15: Part I--Classification
نویسندگان
چکیده
A complete classification of the perfect binary one-error-correcting codes of length 15 as well as their extensions of length 16 is presented. There are 5 983 such inequivalent perfect codes and 2 165 extended perfect codes. Efficient generation of these codes relies on the recent classification of Steiner quadruple systems of order 16. Utilizing a result of Blackmore, the optimal binary one-error-correcting codes of length 14 and the (15, 1 024, 4) codes are also classified; there are 38 408 and 5 983 such codes, respectively.
منابع مشابه
The Perfect Binary One-Error-Correcting Codes of Length 15: Part II--Properties
A complete classification of the perfect binary oneerror-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,” submitted for publication]. In the current accompanying work, the classified codes are studied in great detail, and the...
متن کاملTwo optimal one-error-correcting codes of length 13 that are not doubly shortened perfect codes
The doubly shortened perfect codes of length 13 are classified utilizing the classification of perfect codes in [P.R.J. Österg̊ard and O. Pottonen, The perfect binary one-error-correcting codes of length 15: Part I— Classification, IEEE Trans. Inform. Theory, to appear]; there are 117821 such (13,512,3) codes. By applying a switching operation to those codes, two more (13,512,3) codes are obtain...
متن کاملOn Optimal Binary One-Error-Correcting Codes of Lengths
Best and Brouwer [Discrete Math. 17 (1977), 235– 245] proved that triply-shortened and doubly-shortened binary Hamming codes (which have length 2m − 4 and 2m − 3, respectively) are optimal. Properties of such codes are here studied, determining among other things parameters of certain subcodes. A utilization of these properties makes a computeraided classification of the optimal binary one-erro...
متن کاملOn Optimal Binary One-Error-Correcting Codes of Lengths $2^m-4$ and $2^m-3$
Best and Brouwer [Discrete Math. 17 (1977), 235– 245] proved that triply-shortened and doubly-shortened binary Hamming codes (which have length 2m − 4 and 2m − 3, respectively) are optimal. Properties of such codes are here studied, determining among other things parameters of certain subcodes. A utilization of these properties makes a computeraided classification of the optimal binary one-erro...
متن کاملTwo-Error Correcting Bose-Chaudhuri Codes are Quasi-Perfect
Bose and Chaudhuri (1960) have introduced a class of binary errorcorrecting codes of block length 2 ~ 1, m = 2,3,• • which we refer to here as B-C codes. An efficient decoding scheme has been devised for them by Peterson (1960), and generalized to the natural extension of the B-C Codes to codes in pm symbols by D. Gorenstein and N. Zierler (1960). Two further properties of B-C codes are establi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- IEEE Trans. Information Theory
دوره 55 شماره
صفحات -
تاریخ انتشار 2009