THE κ-GALOIS HULLS OF MULTI-TWISTED CODES: DIMENSION AND GENERATORS CONSTRUCTION

. In the comprehensive class of the multi-twisted (MT) codes over a finite field, we study the Galois hull construction. The Galois hull of an MT code is its intersection with its Galois dual. First, we utilize the generator polynomial matrix (GPM) G of any MT code C to determine the dimension of its Galois hull. Then, we associate a linear code 2G to each GPM G, which we show to be quasi-cyclic. We prove that the product of the GPM of the Galois dual of 2G with G yields a GPM for the Galois hull of C. Special cases of Galois self-orthogonal and Galois linear complementary dual MT codes are also described.