Constructing formally self-dual codes over Rk R k
In this work, we study construction techniques of formally self-dual codes over the infinite family of rings R k = F 2 [ u 1 , u 2 ,  , u k ] / ? u i 2 = 0 , u i u j = u j u i ? . These codes give rise to binary formally self-dual codes. Using these constructions, we obtain a number of good formally self-dual binary codes including even formally self-dual binary codes of parameters [72,36,14] [ 72 , 36 , 14 ] , [56,28,12] [ 56 , 28 , 12 ] , [44,22,10] [ 44 , 22 , 10 ] and odd formally self-dual binary codes of parameters [72,36,13] [ 72 , 36 , 13 ] , all of which have better minimum distances than the best known self-dual codes of the same lengths.
formally self-dual codes codes over rk r k rk r k rk r k r k extremal codes codes over rings