One and Two?Weight ? <sub>2</sub> <i>R</i> <sub>2</sub> Additive Codes
نویسندگان
چکیده
This paper is devoted to the construction of one and two-weight additive codes, where . It a generalization towards another direction codes (S.T. Dougherty, H.W. Liu L. Yu, “One weight codes”, Applicable Algebra in Engineering, Communication Computing, Vol.27, No.2, pp.123-138, 2016). A MacWilliams identity which connects enumerator an code over its dual established. Several methods one-weight are presented. examples presented illustrate our main results some open problems also proposed.
منابع مشابه
Isometries of Additive Codes
(June 15, 2016.) FIX: June 15, 2016. This needs to be re-written. Monomial transformations of linear codes are linear isometries for the Hamming weight. A code alphabet has the extension property for the Hamming weight when every linear isometry between codes extends to a monomial transformation. MacWilliams proved that finite fields have the extension property for the Hamming weight. In contra...
متن کاملZ2Z4-additive cyclic codes, generator polynomials and dual codes
A Z2Z4-additive code C ⊆ Z2 ×Zβ4 is called cyclic if the set of coordinates can be partitioned into two subsets, the set of Z2 and the set of Z4 coordinates, such that any cyclic shift of the coordinates of both subsets leaves the code invariant. These codes can be identified as submodules of the Z4[x]-module Z2[x]/(x− 1)×Z4[x]/(x − 1). The parameters of a Z2Z4-additive cyclic code are stated i...
متن کاملCyclic additive codes and cyclic quantum stabilizer codes
The theory of cyclic linear codes in its ring-theoretic formulation is a core topic of classical coding theory. A simplified approach is in my textbook [1]. The language of ring theory is not needed. We will present a self-contained description of the more general theory of cyclic additive codes using the same method. This includes cyclic quantum stabilizer codes as a special case. The basic in...
متن کاملAdditive Quantum Codes CS191 Project
We study quantum error correction with emphasis on additive codes. We present the uncorrelated error model and paradigm for construction of additive codes. We also review constructions of non-additive codes using additive codes.
متن کاملIsometry Groups of Additive Codes
When C ⊆ F is a linear code over a finite field F, every linear Hamming isometry of C to itself is the restriction of a linear Hamming isometry of F to itself, i.e., a monomial transformation. This is no longer the case for additive codes over non-prime fields. Every monomial transformation mapping C to itself is an additive Hamming isometry, but there exist additive Hamming isometries that are...
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: Chinese Journal of Electronics
سال: 2021
ISSN: ['1022-4653', '2075-5597']
DOI: https://doi.org/10.1049/cje.2020.10.011