Attacks and counter-attacks on the GPT public key cryptosystem
Designs, Codes and Cryptography
Maximum rank distance codes as space-time codes
IEEE Transactions on Information Theory
A Rank-Metric Approach to Error Control in Random Network Coding
IEEE Transactions on Information Theory
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In the theory of codes based on Hamming metric, three classes of codes are well known: cyclic codes, shortened cyclic codes and pseudo-cyclic codes. An important result is that the class of linear shortened cyclic codes coincides with the class of linear pseudo-cyclic codes [1]. No similar results are known in the theory of rank-metric based codes. In this paper, we generalize the notion of q-cyclic codes and introduce two new families of codes, namely, shortened q-cyclic codes and pseudo-q-cyclic codes. It is proved that the class of pseudo-q-cyclic codes coincides with the class of shortened q-cyclic codes if the number of positions to shorten is a multiple of the extension degree. The problem is still open for other shortening.