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On the Covering Radius of Codes over Z p k

Author

Listed:
  • Mohan Cruz

    (Bishop Heber College, Affiliated to Bharathidasan University, Tiruchirappalli 620 017, Tamilnadu, India
    Department of Mathematics, Bharathidasan University, Tiruchirappalli 620 024, Tamilnadu, India
    These authors contributed equally to this work.)

  • Chinnapillai Durairajan

    (Department of Mathematics, Bharathidasan University, Tiruchirappalli 620 024, Tamilnadu, India
    These authors contributed equally to this work.)

  • Patrick Solé

    (CNRS, Aix-Marseille University, Centrale Marseille, I2M, 13009 Marseilles, France
    These authors contributed equally to this work.)

Abstract

In this correspondence, we investigate the covering radius of various types of repetition codes over Z p k ( k ≥ 2 ) with respect to the Lee distance. We determine the exact covering radius of the various repetition codes, which have been constructed using the zero divisors and units in Z p k . We also derive the lower and upper bounds on the covering radius of block repetition codes over Z p k .

Suggested Citation

  • Mohan Cruz & Chinnapillai Durairajan & Patrick Solé, 2020. "On the Covering Radius of Codes over Z p k," Mathematics, MDPI, vol. 8(3), pages 1-10, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:328-:d:327556
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