Codes Induced by Alternative Codes

Abstract

Alternative codes, an extension of the notion of ordinary codes, have been first introduced and considered by Huy and Nam (2004). As seen below, every alternative code, in its turn, defines an ordinary code. Such codes are called codes induced by alternative codes or alt-induced codes, for short. In this paper, we consider these alt-induced codes and subclasses of them. In particular, characteristic properties of such codes are established, and an algorithm to check whether a finite code is alt-induced or not is proposed.

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Acknowledgements

The authors would like to thank the colleagues in the Seminar on Mathematical Foundation of Computer Science at Institute of Mathematics, Vietnam Academy of Science and Technology for attention to this work. Especially, the authors express their sincere thanks to Dr. Nguyen Huong Lam and Dr. Kieu Van Hung for their useful discussions.

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Correspondence to Ngo Thi Hien.

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Hien, N.T., Van, D.L. Codes Induced by Alternative Codes. Acta Math Vietnam 43, 357–371 (2018). https://doi.org/10.1007/s40306-018-0247-2

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Keywords

  • Code
  • Alt-induced code
  • Strong alt-induced code
  • Alternative code
  • Strong alternative code

Mathematics Subject Classification (2010)

  • 94A45
  • 68Q45