A Lower Bound for Generalized Hamming Weights and a Condition for t-th Rank MDS∗
نویسنده
چکیده
In this paper, we introduce a lower bound for the generalized Hamming weights, which is applicable to arbitrary linear code, in terms of the notion of well-behaving. We also show that any [n, k] linear code C over a finite field F is the t-th rank MDS for t such that g(C) + 1 ≤ t ≤ k where g(C) is easily calculated from the basis of F so chosen that whose first n − k elements generate C⊥. Finally, we apply our result to Reed-Solomon, Reed-Muller and algebraic geometry codes on Cab, and determine g(C) for each code. key words: generalized Hamming weights, t-th rank MDS, ReedSolomon codes, Reed-Muller codes, codes on affine algebraic variety, AG codes on Cab
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