On Linear Codes over$${\mathbb{Z}}_{2^{s}}$$
Designs, Codes and Cryptography
Higher Weights for Ternary and Quaternary Self-Dual Codes*
Designs, Codes and Cryptography
On generalized hamming weights and the covering radius of linear codes
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Finite Fields and Their Applications
Moments of the support weight distribution of linear codes
Designs, Codes and Cryptography
Code constructions and existence bounds for relative generalized Hamming weight
Designs, Codes and Cryptography
| Hi-index | 754.84 |
The minimum support weight, dr(C), of a linear code C over GF(q) is the minimal size of the support of an r-dimensional subcode of C. A number of bounds on dr(C) are derived, generalizing the Plotkin bound and the Griesmer bound, as well as giving two new existential bounds. As the main result, it is shown that there exist codes of any given rate R whose ratio dr/d1 is lower bounded by a number ranging from (qr-1)/(qr -qr-1) to r, depending on R