Constructing formally self-dual codes over [formula omitted

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In this work, we study construction techniques of formally self-dual codes over the infinite family of rings Rk=F2[u1,u2,…,uk]/〈ui2=0,uiuj=ujui〉. 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], [56,28,12], [44,22,10] and odd formally self-dual binary codes of parameters [72,36,13], all of which have better minimum distances than the best known self-dual codes of the same lengths.