Optimal binary linear codes of dimension at most seven Original Research Article

We classify optimal [n,k,d] binary linear codes of dimension ⩽7, with one exception, where by optimal we mean that no [n−1,k,d], [n+1,k+1,d], or [n+1,k,d+1] code exists. In particular, we present (new) classification results for codes with parameters [40,7,18], [43,7,20], [59,7,28], [75,7,36], [79,7,38], [82,7,40], [87,7,42], and [90,7,44]. These classifications are accomplished with the aid of the first authorʹs computer program Extension for extending from residual codes, and the second authorʹs program Split.