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An Upper Bound of Singleton Type for Componentwise Products of Linear Codes

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1 Author(s)
Randriambololona, H. ; LTCI, Ecole Nat. Super. des Telecommuncations (“Telecom ParisTech”), Paris, France

We give an upper bound that relates the dimensions of some given number of linear codes, with the minimum distance of their componentwise product. A typical result is as follows: given t linear codes Ci of parameters [n,ki]q with full support, one can find codewords ci ∈ Ci such that 1 ≤ w(c1*⋯*ct) ≤ max(t-1, n+t-(k1+⋯+kt)).

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Information Theory, IEEE Transactions on  (Volume:59 ,  Issue: 12 )