On the Preparata-like codes
نویسندگان
چکیده
A class of Preparata-like group codes is considered. It was suggested by Baker, van Lint and Wilson and re-stated in a different form by Ericson. We show that all such codes are inside the Hamming code providing its partition into the cosets of the Preparata-like codes. This partition induces 2-resolvable Steiner quadruple systems.
منابع مشابه
On perfect codes that do not contain Preparata-like codes
We show that for every length of form 4 k − 1, there exists a binary 1-perfect code that does not include any Preparata-like code.
متن کاملOn the automorphism groups of the Z2 Z4 -linear 1-perfect and Preparata-like codes
We consider the symmetry group of a Z2Z4-linear code with parameters of a 1-perfect, extended 1-perfect, or Preparata-like code. We show that, provided the code length is greater than 16, this group consists only of symmetries that preserve the Z2Z4 structure. We find the orders of the symmetry groups of the Z2Z4-linear (extended) 1-perfect codes.
متن کاملOn the kernel and rank of Z 4 - linear Preparata - like and Kerdock - like codes ∗
We say that a binary code of length n is additive if it is isomorphic to a subgroup of Z2 ×Zβ4 , where the quaternary coordinates are transformed to binary by means of the usual Gray map and hence α + 2β = n. In this paper we prove that any additive extended Preparata-like code always verifies α = 0, i.e. it is always a Z4-linear code. Moreover, we compute the rank and the dimension of the kern...
متن کاملOn the Apparent Duality of the Kerdock and Preparata Codes
The Kerdock and extended Preparata codes are something of an enigma in coding theory since they are both Hamming-distance invariant and have weight enumerators that are MacWilliams duals just as if they were dual linear codes. In this paper, we explain, by constructing in a natural way a Preparata-like code PL from the Kerdock code K, why the existence of a distance-invariant code with weight d...
متن کاملThe Preparata and Goethals codes: Trellis complexity and twisted squaring constructions
The trellis complexity of the Preparata and Goethals codes is examined. It is shown that at least for a given set of permutations these codes are rectangular. Upper bounds on the state complexity profiles of the Preparata and Goethals codes are given. The upper bounds on the state complexity of the Preparata and Goethals codes are determined by the DLP of the extended primitive doubleand triple...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014