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. 1 Background A linear code is a normed space and the weights (or norms) of codewords are crucial for the code’s performance. One of the most important parameters of a code is the minimum distance or minimum weight of a codeword. The concept of weights can be generalised to subcodes or even arbitrary subsets of the code. (This is often called support weights or support sizes.) One of the key papers is [Wei91], where Wei defined the rth generalised Hamming weight to be the least weight of a r-dimensional subcode. After Wei’s work, we have seen many attempts to determine the generalised Hamming weights of different...

• Type: Conference
• Year: 2001
• Where: AAECC
• Authors: Hans Georg Schaathun
• Keywords: AAECC 2001, Algorithms, Generalised, Hamming Weights, Projective Multisets