Update on the Extension of Good Linear Codes

In this short note we state how we construct new good linear codes C over the finite field with q elements. We start with already good (= high minimum distance d for given length n and dimension k) codes which we got for example by our method [2,3,4,5]. The advantage of this method is that we explictly get the words of minimum weight d. We try to extend the generator matrix of C by adding columns with the property that at least s of the letters added to the codewords are different from 0.Using this we know that the minimum distance of the extended code is d + s as long as the second smallest weight was ≥ d + s. In this note we only state the method and the results. A full version [8] is submitted to the proceedings of Combinatorics 2006.