Quadratic form Approach for the Number of Zeros of Homogeneous Linear Recurring Sequences over Finite Fields

  •  Yasanthi Kottegoda    


We consider homogeneous linear recurring sequences over a finite field $\mathbb{F}_{q}$, based on an irreducible characteristic polynomial of degree $n$ and order $m$. Let $t=(q^{n}-1)/ m$. We use quadratic forms over finite fields to give the exact number of occurrences of zeros of the sequence within its least period when $t$ has q-adic weight 2. Consequently we prove that the cardinality of the set of zeros for sequences from this category is equal to two.

This work is licensed under a Creative Commons Attribution 4.0 License.
  • ISSN(Print): 1916-9795
  • ISSN(Online): 1916-9809
  • Started: 2009
  • Frequency: bimonthly

Journal Metrics

  • h-index (February 2019): 18
  • i10-index (February 2019): 48
  • h5-index (February 2019): 7
  • h5-median (February 2019): 10

( The data was calculated based on Google Scholar Citations. Click Here to Learn More. )