Coding in Term-rank Metric

This paper investigates coding for crisscross errors in the term-rank metric. The term-rank of a matrix equals to minimal number of row and columns that collectively contain all of non zero elements of the matrix. We consider data stored in arrays (matrices) over finite fields. Crisscross errors occur e.g. in memory arrays, FSK demodulation, magnetic tapes or in OFDM and FDM transmissions. In the paper, we introduce construction of term-rank codes with different distances. Also, we investigate polynomial-time decoding for term-rank codes. Research results derived from the paper show that the term-rank metric is more suitable than the rank metric for correcting crisscross errors.