New decoding algorithms for super-symmetric rank codes

New decoding algorithms for the super-symmetric rank codes [1] are constructed. They include the recurrent decoding algorithm and the majority decoding algorithm. The super-symmetric rank codes are rank-metric codes over binary fields with lengths N
s
= 2
^s
, s = 0, 1, …, where codes of length N
s
are designed recursively from codes of length N
−1
. This provides block symmetry construction of code matrices and allows to decode corrupted received matrices starting with a small size. The new decoding algorithms are described and simulation results are presented.