The Weight Hierarchy of Hermitian Codes
SIAM Journal on Discrete Mathematics
On Generalized Hamming Weights of Codes Constructed on Affine Algebraic Sets
AAECC-12 Proceedings of the 12th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
On the feng-rao bound for generalized hamming weights
AAECC'06 Proceedings of the 16th international conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Improved geometric Goppa codes. I. Basic theory
IEEE Transactions on Information Theory - Part 1
Generalized Hamming weights of q-ary Reed-Muller codes
IEEE Transactions on Information Theory
Polynomial weights and code constructions
IEEE Transactions on Information Theory
Generalized Hamming weights for linear codes
IEEE Transactions on Information Theory
A simple approach for construction of algebraic-geometric codes from affine plane curves
IEEE Transactions on Information Theory
On puncturing of codes from Norm--Trace curves
Finite Fields and Their Applications
On codes from norm-trace curves
Finite Fields and Their Applications
On the Structure of Order Domains
Finite Fields and Their Applications
Generalized Sudan's list decoding for order domain codes
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Improved evaluation codes defined by plane valuations
Finite Fields and Their Applications
Weighted Reed---Muller codes revisited
Designs, Codes and Cryptography
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The celebrated Feng-Rao bound estimates the minimum distance of codes defined by means of their parity check matrices. From the Feng-Rao bound it is clear how to improve a large family of codes by leaving out certain rows in their parity check matrices. In this paper we derive a simple lower bound on the minimum distance of codes defined by means of their generator matrices. From our bound it is clear how to improve a large family of codes by adding certain rows to their generator matrices. The new bound is very much related to the Feng-Rao bound as well as to Shibuya and Sakaniwa's bound in [T. Shibuya, K. Sakaniwa, A dual of well-behaving type designed minimum distance, IEICE Trans. Fund. E84-A (2001) 647-652]. Our bound is easily extended to deal with any generalized Hamming weights. We interpret our methods into the setting of order domain theory. In this way we fill in an obvious gap in the theory of order domains.