On nonsystematic perfect binary codes of length 15
نویسندگان
چکیده
منابع مشابه
Properties of perfect transitive binary codes of length 15 and extended perfect transitive binary codes of length 16
Properties of perfect transitive binary codes of length 15 and extended perfect transitive binary codes of length 16 Abstract. Some properties of perfect transitive binary codes of length 15 and extended perfect transitive binary codes of length 16 are presented for reference purposes. The attached files contain some tab-delimited properties of perfect binary codes of length 15 and extended per...
متن کاملThe Perfect Binary One-Error-Correcting Codes of Length 15: Part I--Classification
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-er...
متن کاملThe 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 کاملAn enumeration of 1-perfect binary codes
We enumerate the extended perfect I-error correcting binary codes of length 16 which can be constructed by the concatenation or doubling construction. In the process, we establish some properties of these codes and consider algorithms that effectively establish the nonequivalence of these codes.
متن کاملRanks of propelinear perfect binary codes
It is proven that for any numbers n = 2 m − 1, m ≥ 4 and r, such that n − log(n + 1) ≤ r ≤ n excluding n = r = 63, n = 127, r ∈ {126, 127} and n = r = 2047 there exists a propelinear perfect binary code of length n and rank r.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2004
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(02)00309-8