Abstract Algebra pp 57-72 | Cite as

# Linear Algebra and Linear Codes

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## Abstract

In this chapter we review the main ideas of linear algebra. The one twist is that we allow our scalars to come from any field instead of just the field of real numbers. In particular, the notion of a vector space over the field \(\mathbb{Z}_{2}\) will be essential in our study of coding theory. We will also need to look at other finite fields when we discuss Reed–Solomon codes. One benefit to working with finite dimensional vector spaces over finite fields is that all sets in question are finite, and so computers can be useful in working with them.

## References

- 1.Halmos P (1987) Finite dimensional vector spaces, 2nd edn. Undergraduate texts in mathematics. Springer, New YorkGoogle Scholar
- 2.Herstein I (1975) Topics in algebra, 2nd edn. Wiley, HobokenzbMATHGoogle Scholar

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© Springer International Publishing Switzerland 2014