Automorphisms and Encoding of AG and Order Domain Codes
نویسنده
چکیده
We survey some encoding methods for AG codes, focusing primarily on one approach utilizing code automorphisms. If a linear code C over Fq has a finite abelian group H as a group of automorphisms, then C has the structure of a module over a polynomial ring P. This structure can be used to develop systematic encoding algorithms using Gröbner bases for modules. We illustrate these observations with several examples including geometric Goppa codes and codes from order domains.
منابع مشابه
The Largest Cap in AG(4, 4) and Its Uniqueness
We show that 40 is the maximum number of points of a cap in AG(4, 4). Up to semi-linear transformations there is only one such 40-cap. Its group of automorphisms is a semidirect product of an elementary abelian group of order 16 and the alternating group A5.
متن کاملBinary extremal self-dual codes of type II and their automorphisms
Binary extremal self-dual codes of type II and their automorphisms Wolfgang Willems Otto-von-Guericke-Universität Magdeburg Extremal type II codes are for several reasons of particular interest. However only for small lengths such codes have been contructed. In order to find larger examples ’symmetries’ or in other words ’non-trivial automorphisms’ may be helpful. In this spirit the talk deals ...
متن کاملOD-characterization of $U_3(9)$ and its group of automorphisms
Let $L = U_3(9)$ be the simple projective unitary group in dimension 3 over a field with 92 elements. In this article, we classify groups with the same order and degree pattern as an almost simple group related to $L$. Since $Aut(L)equiv Z_4$ hence almost simple groups related to $L$ are $L$, $L : 2$ or $L : 4$. In fact, we prove that $L$, $L : 2$ and $L : 4$ are OD-characterizable.
متن کاملIdentification of effectiveness assessment criteria for Seminary virtual courses
The main purpose of this research is to derive Seminary virtual education effectiveness criteria. Seminary education has main differences with tertiary or professional education. Therefore, to assess their effectiveness, we must take into account these differences. In this research we have used qualitative methodology and set a semi-interview mechanism with 15 experts in e-learning, all employe...
متن کاملOn the automorphism groups of some AG-codes based on Ca, b curves
We study Ca,b curves and their applications to coding theory. We show how Ca,b curves can be used to construct MDS codes and focus on some Ca,b curves with extra automorphisms, namely y 3 = x + 1, y = x − x, y − y = x. The automorphism groups of such codes are determined in most characteristics.
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 2007