Which integer sequences are sequences of generalized weights of a linear code? In this paper, we answer this question for linear block codes, rank-metric codes, and more generally for sum-rank metric codes. We do so under an existence assumption for MDS and MSRD codes. We also prove that the same integer sequences appear as sequences of greedy weights of linear block codes, rank-metric codes, and sum-rank metric codes. Finally, we characterize the integer sequences which appear as sequences of relative generalized weights (respectively, relative greedy weights) of linear block codes.

翻译：哪些整数序列可以作为线性码的广义权序列？本文回答了线性分组码、秩度量码以及更一般的和秩度量码的这一问题。我们在假设MDS码和MSRD码存在的前提下进行讨论。同时证明，相同的整数序列也可以作为线性分组码、秩度量码和和秩度量码的贪婪权序列出现。最后，我们刻画了能够作为线性分组码的相对广义权（以及相对贪婪权）序列出现的整数序列。