Problem sheet 10 2005, March. 17

MT361 Error correcting codes

Ex. 1 Show that the Latin squares L_{1} and L_{3} of order 4 are not orthogonal. Construct two orthogonal Latin Squares of order 4 as follows: Construct the field of 4 elements by taking all polynomials with coefficients 0 and 1, and reduce modulo x^{2} + x + 1. Show that the 4 elements are: 0, 1, x, x + 1. Write down the addition and multiplication table of this field. From this find two MOLS of order 4. Bring them into standard form.