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**2022/966**

**Title:**

On Linear Complexity of Finite Sequences : Coding Theory and Applications to Cryptography

**Authors:**
Edoardo Persichetti and Tovohery Randrianarisoa

**Abstract:**

We define two metrics on vector spaces over a finite field using the linear complexity of finite sequences. We then develop coding theory notions for these metrics and study their properties. We give a Singleton-like bound as well as constructions of subspaces achieving this bound. We also provide an asymptotic Gilbert-Varshamov-like bound for random subspaces. We show how to reduce the problem of finding codewords with given Hamming weight into a problem of finding a vector of a given linear complexity. This implies that our new metric can be used for cryptography in a similar way to what is currently done in the code-based setting.

**ePrint:**
https://eprint.iacr.org/2022/966

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