Constructing critical indecomposable codes

Critical indecomposable codes were introduced by Assmus [1], who also gave a recursive construction for these objects. One of the key ingredients in t he construction is an auxiliary code, which is an indecomposable code of mi nimum distance at least 3, In terms of actually being able to construct all critical indecomposable codes, however, Assmus leaves many unanswered ques tions about these auxiliary codes. In this paper, we provide answers to the se questions, including a description of when two equivalent auxiliary code s can yield inequivalent critical indecomposable codes, and results on both the minimum length and the maximum number of critical columns of an auxili ary code. We end with an enumeration of all critical indecomposable codes o f dimension at most 10.