You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
A statistical estimation algorithm of the weight distribution of a linear code is shown, based on using its generator matrix as a compression function on random bit strings.

Cited Abstract(s):
[1]: Decoding random linear codes is a fundamental problem in complexity theory and lies at the heart of almost all code-based cryptography. The best attacks on the most prominent code-based cryptosystems such as McEliece directly use decoding algorithms for linear codes. The asymptotically best decoding algorithm for random linear codes of length n was for a long time Stern’s variant of information-set decoding running in time O 20.05563n . Recently, Bernstein, Lange and Peters proposed a new technique called Ball-collision decoding which offers a speed-up over Stern’s algorithm by improving the running time to O 20.05558n . In this paper, we present a new algorithm for decoding linear codes that is inspired by a representation technique due to Howgrave-Graham and Joux in the context of subset sum algorithms. Our decoding algorithm offers a rigorous complexity analysis for random linear codes and brings the time complexity down to O 20.05363n .
The Lee-Brickell algorithm can be written as follows (see [1] ): Compute the permuted syndrome @math . Fix a weight @math . If then we can choose another set @math of @math columns from @math to obtain a set @math of columns of @math that sum to @math . Otherwise, restart with a different @math .