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  • Bounds on the distance of cyclic codes  (1)
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    Electronic Resource
    Electronic Resource
    Divisibility properties and new bounds for cyclic codes and exponential sums in one and several variables (1994)
    Springer
    Applicable algebra in engineering, communication and computing 5 (1994), S. 105-116 
    Details
    ISSN: 1432-0622
    Keywords: Bounds on the distance of cyclic codes ; Divisible codes ; Exponential sums
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics , Technology
    Notes: Abstract Serre has obtained sharp estimates for the number of rational points on an algebraic curve over a finite field. In this paper we supplement his technique with divisibility properties for exponential sums to derive new bounds for exponential sums in one and several variables. The new bounds give us an improvement on previous bounds for the minimum distance of the duals of BCH codes. The divisibility properties also imply the existence of gaps in the weight distribution of certain cyclic codes, and in particular gives us that BCH codes are divisible (in the sense of H. N. Ward).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01438279
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