# Introduction to coding theory (CMU, Spr 2010)

## February 3, 2010

### Lecture 7 summary

Filed under: Lecture summary — Venkat Guruswami @ 5:57 pm

We discussed the basics of the Discrete Fourier Transform over the hypercube, and used it to derive the MacWilliams identities relating the weight distribution of a binary linear code to that of its dual. This led to a linear program whose optimum was an upper bound for the size of linear codes of certain distance. We then saw that the same linear program is also valid for all codes, and thus its optimum bounds $A(n,d)$ from above. We wrote the dual of this linear program and noted that any dual feasible solution gives a valid upper bound on $A(n,d)$.