On the orphans and covering radius of the reed-muller codes

  • Philippe Langevin
Submitted Contributions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 539)


In [4] is given an inductive proof of the existence of families of orphans of RM(1, m) whose weight distributions are {2m−1 − ∈2(m+k−2)/2 | ∈ = −1, 0, 1}, where k satisfies 0≤k<m and km (mod 2). We show that any coset of RM(1, m) having this kind of distribution is an orphan. In particular, the coset of a not completely degenerate quadratic form is always an orphan. Working about the conjecture which says that the covering radius of RM(1, m) is even, we prove that an orphan of odd weight of RM(1, m) cannot be 0-covered. Finally, we simplify our proof, given in [5], that the distance from any cubic of RM(3, 9) to RM(1, 9) is at most 240.


Quadratic Form Boolean Function Binary Code Covering Radius Inductive Proof 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Philippe Langevin
    • 1
  1. 1.G. E. C. T. Université de ToulonLa GardeFrance

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