A dual of well-behaving type designed minimum distance

Evaluation codes from order domain theory

“…In this language already one bound is known that deals with the minimum distance of codes defined by means of their generator matrix. This is the for too little recognized bound by Shibuya and Sakaniwa in [26]. The bound that we derive in the present paper is very much related to Shibuya and Sakaniwa's bound.…”

On the Feng-Rao Bound for Generalized Hamming Weights

“…In [19] Shibuya and Sakaniwa considered the set-up with only one basis B (that is, the setup in Theorem 1 with B = B ). In [19] they were concerned with the WWB property.…”

“…In [19] they were concerned with the WWB property. In [20] Shibuya and Sakaniwa considered the set-up with two bases B, B but were only concerned with the WB property.…”

“…, b is }. The Shibuya-Sakaniwa bound from [19] and [20] can be interpreted as follows (we have replaced their WB respectively WWB with OWB).…”

“…However, it was not described in [7] how to deal with the Feng-Rao improved codes. In the series of papers [15], [16], [17], [18], [19], [20], Shibuya, Sakaniwa et. al derived a bound on the generalized Hamming weights of linear codes defined by means of their parity check matrices.…”