Gröbner Bases for Schubert Codes
نویسندگان
چکیده
We consider the problem of determining Gröbner bases of binomial ideals associated with linear error correcting codes. Computation of Gröbner bases of linear codes have become a topic of interest to many researchers in coding theory because of its several applications in decoding and error corrections. In this paper, Gröbner bases of linear codes associated to Grassmann varieties and Schubert varieties over a binary field have been obtained. We also use them to study the decoding of binary Schubert codes.
منابع مشابه
A General Framework for Applying FGLM Techniques to Linear Codes
We show herein that a pattern based on FGLM techniques can be used for computing Gröbner bases, or related structures, associated to linear codes. This Gröbner bases setting turns out to be strongly related to the combinatorics of the codes.
متن کاملGröbner geometry of Schubert polynomials
Schubert polynomials, which a priori represent cohomology classes of Schubert varieties in the flag manifold, also represent torus-equivariant cohomology classes of certain determinantal loci in the vector space of n×n complex matrices. Our central result is that the minors defining these “matrix Schubert varieties” are Gröbner bases for any antidiagonal term order. The Schubert polynomials are...
متن کاملFe b 20 02 Gröbner geometry of Schubert polynomials
Schubert polynomials, which a priori represent cohomology classes of Schubert varieties in the flag manifold, also represent torus-equivariant cohomology classes of certain determinantal loci in the vector space of n×n complex matrices. Our central result is that the minors defining these “matrix Schubert varieties” are Gröbner bases for any antidiagonal term order. The Schubert polynomials are...
متن کاملEfficient decoding of (binary) cyclic codes above the correction capacity of the code using Gröbner bases
This paper revisits the topic of decoding cyclic codes with Gröbner bases. We introduce new algebraic systems, for which the Gröbner basis computation is easier. We show that formal decoding formulas are too huge to be useful, and that the most efficient technique seems to be to recompute a Gröbner basis for each word (online decoding). We use new Gröbner basis algorithms and “trace preprocessi...
متن کاملGraver Bases and Universal Gröbner Bases for Linear Codes
Linear codes over any finite field can be associated to binomial ideals. Focussing on two specific instances, called the code ideal and the generalized code ideal, we present how these binomial ideals can be computed from toric ideals by substituting some variables. Drawing on this result we further show how their Graver bases as well as their universal Gröbner bases can be computed.
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:
- CoRR
دوره abs/1707.02199 شماره
صفحات -
تاریخ انتشار 2017