Codes and Projective Multisets

نویسندگان

  • Stefan M. Dodunekov
  • Juriaan Simonis
چکیده

The paper gives a matrix-free presentation of the correspondence between full-length linear codes and projective multisets. It generalizes the BrouwerVan Eupen construction that transforms projective codes into two-weight codes. Short proofs of known theorems are obtained. A new notion of self-duality in coding theory is explored. 94B05, 94B27, 51E22.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Linear Codes over Finite Chain Rings

The aim of this paper is to develop a theory of linear codes over finite chain rings from a geometric viewpoint. Generalizing a well-known result for linear codes over fields, we prove that there exists a one-to-one correspondence between so-called fat linear codes over chain rings and multisets of points in projective Hjelmslev geometries, in the sense that semilinearly isomorphic codes corres...

متن کامل

Duality and Greedy Weights of Linear Codes and Projective Multisets

A projective multiset is a collection of projective points, which are not necessarily distinct. A linear code can be represented as a projective multiset, by taking the columns of a generator matrix as projective points. Projective multisets have proved very powerful in the study of generalised Hamming weights. In this paper we study relations between a code and its dual.

متن کامل

Canonical Forms and Automorphisms in the Projective Space

Let C be a sequence of multisets of subspaces of a vector space Fq . We describe a practical algorithm which computes a canonical form and the stabilizer of C under the group action of the general semilinear group. It allows us to solve canonical form problems in coding theory, i.e. we are able to compute canonical forms of linear codes, Fq-linear block codes over the alphabet Fqs and random ne...

متن کامل

Ring geometries, two-weight codes, and strongly regular graphs

It is known that a linear two-weight code C over a finite field Fq corresponds both to a multiset in a projective space over Fq that meets every hyperplane in either a or b points for some integers a < b , and to a strongly regular graph whose vertices may be identified with the codewords of C . Here we extend this classical result to the case of a ring-linear code with exactly two nonzero homo...

متن کامل

Intersection sets, three-character multisets and associated codes

In this article we construct new minimal intersection sets in AG(r, q2) sporting three intersection numbers with hyperplanes; we then use these sets to obtain linear error correcting codes with few weights, whose weight enumerator we also determine. Furthermore, we provide a new family of three-character multisets in PG(r, q2) with r even and we also compute their weight distribution.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • Electr. J. Comb.

دوره 5  شماره 

صفحات  -

تاریخ انتشار 1998