Let C be an [n, k, d]-code over GF(q) with k greater than or equal to 2. Let s = def(C) = n + 1 - k - d denote the defect of C. The Griesmer bound implies that d less than or equal to q(s + 1). If d > qs and s greater than or equal to 2, then using a previous result of Faldum and Willems, k less than or equal to q, Thus fixing s greater than or equal to 2 the extreme parameters for a code with
... [Show full abstract] def(C) = s are d = q(s + 1), k = q, and n = k + d + s - 1 = (q + 1)(s + 2) - 3, In this correspondence we characterize the codes with such parameters.