Noncyclic Generalizations of BCH and Srivastava Codes

We define two classes of linear error correcting codes which are noncyclic generalizations of the well known BCH and Srivastava codes. The corresponding parity check matrices are basically alternating functions of certain elements of GF(qm) and all determinants of maximum order of the parity check matrices are alternants. As a consequence lower bounds on the minimum distance of these codes can easily be obtained.

[1]  B. Igel.  Zur Theorie der Determinanten , 1892 .

[2]  Elwyn R. Berlekamp,et al.  Algebraic coding theory , 1984, McGraw-Hill series in systems science.

[3]  Dwijendra K. Ray-Chaudhuri,et al.  Binary mixture flow with free energy lattice Boltzmann methods , 2022, arXiv.org.