Application of hyperplane arrangements to error-correcting codes
Talk by Dr. Relinde Jurrius
Date: 23.11.16 Time: 16.00 - 17.00 Room:
Linear error-correcting codes are closely connected to hyperplane arrangements: the columns of the generator matrix of a code can be viewed as the coordinates of a hyperplane arrangement over a finite field. Using this correspondence, one can transform counting problems about linear codes, such as weight enumeration, to counting problems on a hyperplane arrangement. In this talk we will see two examples of that. First we discuss the weight enumerator, an important polynomial invariant of a code. The weight enumerator has a straightforward relation to the characteristic polynomials of an arrangement. The second example focusses on recent work on the coset weight enumerator, and has more open questions.