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Construction of Observable and MDP Convolutional Codes with Good Decodable Properties by ISO Representations Cover

Construction of Observable and MDP Convolutional Codes with Good Decodable Properties by ISO Representations

Open Access
|Mar 2026

References

  1. Allen, B. (1999). Linear Systems Analysis and Decoding of Convolutional Codes, Thesis dissertation, University of Notre Dame, Notre Dame http://user.math.uzh.ch/rosenthal/Paper/ThesisBrian.pdf.
  2. Almeida, P.J., Napp, D. and Pinto, R. (2016). Superregular matrices and applications to convolutional codes, Linear Algebra and Its Applications 499: 1–25.
  3. Climent, J.-J., Herranz, V. and Perea, C. (2007). A first approximation of concatenated convolutional codes from linear systems theory viewpoint, Linear Algebra and Its Applications 425(2): 673–699.
  4. Climent, J.-J., Napp, D., Pinto, R. and Requena, V. (2021). Minimal state-space representation of convolutional product codes, Mathematics 9(12): 1410.
  5. Climent, J.-J., Napp, D., Pinto, R. and Simóes, R. (2018). Series concatenation of 2D convolutional codes by means of input-state-output representations, International Journal of Control 91(12): 2682–2691, DOI: 10.1080/00207179.2017.1410573.
  6. Climent, J.-J., Napp, D. and Requena, V. (2025). An algorithm to compute a minimal input-state-output representation of a convolutional code, Linear Algebra and Its Applications 721: 715–735.
  7. DeCastro-García, N. and García-Planas, M.I. (2018). Concatenated linear systems over rings and their application to construction of concatenated families of convolutional codes, Linear Algebra and Its Applications 542: 624–647.
  8. Elias, P. (1955). Coding for two noisy channels, IRE WESCON Convention Record 4: 37–46.
  9. Falb, P. (1999). Methods of Algebraic Geometry in Control Theory. Part II: Multivariable Linear Systems and Projective Algebraic Geometry, Systems & Control: Foundations & Applications, Birkhäuser, Boston.
  10. Forney, G. (1970). Convolutional codes I: Algebraic structure, IEEE Transactions on Information Theory 16(6): 720–738.
  11. García-Planas, M. and Domínguez-García, J. (2013). Alternative tests for functional and pointwise output-controllability of linear time-invariant systems, Systems & Control Letters 62(5): 382–387.
  12. García-Planas, M., Souidi, E.M. and Um, L. (2013). Convolutional codes under control theory point of view: Analysis of output-observability, 12th WSEAS International Conference on Recent Advances in Circuits, Communications and Signal Processing, Cambridge, UK, pp. 131–137.
  13. García-Planas, M., Souidi, E. and Um, L. (2014). Decoding algorithm for convolutional codes under linear systems point of view, 8th WSEAS International Conference on Recent Advances in Circuits, Systems, Signal Processing and Communications, Tenerife, Spain, pp. 17–24.
  14. Gluesing-Luerssen, H., Rosenthal, J. and Smarandache, R. (2006). Strongly-MDS convolutional codes, IEEE Transactions on Information Theory 52(2): 584–598.
  15. Hazewinkel, M. and Kalman, R.E. (1976). On invariants, canonical forms and moduli for linear, constant, finite dimensional, dynamical systems, in G. Marchesini and S.K. Mitter (Eds), Mathematical Systems Theory, Springer, Berlin/Heidelberg, pp. 48–60.
  16. Hutchinson, R., Rosenthal, J. and Smarandache, R. (2005). Convolutional codes with maximum distance profile, Systems & Control Letters 54(1): 53–63.
  17. Kuriata, E. (2008). Creation of unequal error protection codes for two groups of symbols, International Journal of Applied Mathematics and Computer Science 18(2): 251–257, DOI: 10.2478/v10006-008-0023-x.
  18. Lieb, J. (2019). Complete MDP convolutional codes, Journal of Algebra and Its Applications 18(6): 1950105.
  19. Lieb, J. and Rosenthal, J. (2021). Erasure decoding of convolutional codes using first-order representations, Mathematics of Control, Signals, and Systems 33: 499–513.
  20. Martín Sánchez, S. and Plaza-Martín, F.J. (2022). A decoding algorithm for convolutional codes, Mathematics 10(9): 1573.
  21. McEliece, R.L. (1998). The algebraic theory of convolutional codes, in V.S. Pless and W.C. Huffman (Eds), Handbook of Coding Theory I, Amsterdam, Elsevier, pp. 1065–1138.
  22. Muñoz Castañeda, A.L., Muñoz-Porras, J.M. and Plaza-Martín, F.J. (2019). Rosenthal’s decoding algorithm for certain 1-dimensional convolutional codes, IEEE Transactions on Information Theory 65(12): 7736–7741.
  23. Muñoz Castañeda, A.L. and Plaza-Martín, F.J. (2021). On the existence and construction of maximum distance profile convolutional codes, Finite Fields and Their Applications 75: 101877.
  24. Napp, D., Perea, C. and Pinto, R. (2010). Input-state-output representations and constructions of finite support 2D convolutional codes, Advances in Mathematics of Communications 4(4): 533–545.
  25. Napp, D., Pereira, R., Pinto, R. and Rocha, P. (2019). Realization of 2D (2,2)-periodic encoders by means of 2D periodic separable Roesser models, International Journal of Applied Mathematics and Computer Science 29(3): 527–539, DOI: 10.2478/amcs-2019-0039.
  26. Napp, D., Pereira, R. and Rocha, P. (2017). A state space approach to periodic convolutional codes, inÁ. Barbero et al. (Eds), Coding Theory and Applications, Lecture Notes in Computer Science, Vol. 10495, Springer, Cham, pp. 238–247, DOI: 10.1007/978-3-319-66278-720.
  27. Pinto, R. and Simôes, R. (2017). On minimality of ISO representation of basic 2D convolutional codes, inÁ. Barbero et al. (Eds), Coding Theory and Applications, Lecture Notes in Computer Science, Vol. 10495, Springer, Cham, pp. 357-271, DOI: 10.1007/978-3-319-66278-722.
  28. Rosenthal, J. (1999). An algebraic decoding algorithm for convolutional codes, in G. Picci and D.S. Gilliam (Eds), Dynamical Systems, Control, Coding, Computer Vision, Birkhäuser, Basel, pp. 343–360, DOI: 10.1007/978-3-0348-8970-416.
  29. Rosenthal, J., Schumacher, J. and York, E. (1996). On behaviors and convolutional codes, IEEE Transactions on Information Theory 42(6): 1881–1891.
  30. Rosenthal, J. and Smarandache, R. (1999). Maximum distance separable convolutional codes, Applicable Algebra in Engineering, Communication and Computing 10(1): 15–32.
  31. Rosenthal, J. and York, F. (1999). BCH convolutional codes, IEEE Transactions on Information Theory 45(6): 1833–1844.
  32. Tomás, V. (2010). Complete-MDP Convolutional Codes over the Erasure Channel, Thesis dissertation, University of Alicante, Alicante, https://rua.ua.es/dspace/bitstream/10045/18325/1/tesis_Tomas.pdf.
  33. Tomás, V., Rosenthal, J. and Smarandache, R. (2012). Decoding of convolutional codes over the erasure channel, IEEE Transactions on Information Theory 58(1): 90–108.
  34. York, E. (1997). Algebraic Description and Construction of Error Correcting Codes: A Systems Theory Point of View, Thesis dissertation, University of Notre Dame, Notre Dame.
DOI: https://doi.org/10.61822/amcs-2026-0011 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
Language: English
Page range: 141 - 154
Submitted on: May 25, 2025
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Accepted on: Sep 9, 2025
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Published on: Mar 21, 2026
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2026 Noemí Decastro-García, Miguel V. Carriegos, Ángel Luis Muñoz Castañeda, published by University of Zielona Góra
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.