Higher Weights of Affine Grassmann Codes and Their Duals
نویسندگان
چکیده
We consider the question of determining the higher weights or the generalized Hamming weights of affine Grassmann codes and their duals. Several initial as well as terminal higher weights of affine Grassmann codes of an arbitrary level are determined explicitly. In the case of duals of these codes, we give a formula for many initial as well as terminal higher weights. As a special case, we obtain an alternative simpler proof of the formula of Beelen et al for the minimum distance of the dual of an affine Grasmann code.
منابع مشابه
The structure of dual Grassmann codes
In this article we study the duals of Grassmann codes, certain codes coming from the Grassmannian variety. Exploiting their structure, we are able to count and classify all their minimum weight codewords. In this classification the lines lying on the Grassmannian variety play a central role. Related codes, namely the affine Grassmann codes, were introduced more recently in [1], while their dual...
متن کاملHigher Weights of Grassmann Codes
Using a combinatorial approach to studying the hyperplane sections of Grassmannians, we give two new proofs of a result of Nogin concerning the higher weights of Grassmann codes. As a consequence, we obtain a bound on the number of higher dimensional subcodes of the Grassmann code having the minimum Hamming norm. We also discuss a generalization of Grassmann codes .
متن کاملHigher weights of Grassmann codes in terms of properties of Schubert unions
We describe the higher weights of the Grassmann codes G(2, m) over finite fields Fq in terms of properties of Schubert unions, and in each case we determine the weight as the minimum of two explicit polynomial expressions in q.
متن کاملLinear codes with complementary duals related to the complement of the Higman-Sims graph
In this paper we study codes $C_p(overline{{rm HiS}})$ where $p =3,7, 11$ defined by the 3- 7- and 11-modular representations of the simple sporadic group ${rm HS}$ of Higman and Sims of degree 100. With exception of $p=11$ the codes are those defined by the row span of the adjacency matrix of the complement of the Higman-Sims graph over $GF(3)$ and $GF(7).$ We show that these codes ha...
متن کاملDecomposable subspaces, linear sections of Grassmann varieties, and higher weights of Grassmann codes
Given a homogeneous component of an exterior algebra, we characterize those subspaces in which every nonzero element is decomposable. In geometric terms, this corresponds to characterizing the projective linear subvarieties of the Grassmann variety with its Plücker embedding. When the base field is finite, we consider the more general question of determining the maximum number of points on sect...
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/1503.02196 شماره
صفحات -
تاریخ انتشار 2015