# REMARK OF Pi,k ON ELLIPTIC CURVES AND APPLICATION FOR MANCHESTER CODING

• Kim, Dae-Yeoul (National Institute for Mathematical Sciences) ;
• Kim, Min-Soo (Department of Mathematics, KAIST)
• Accepted : 2011.04.05
• Published : 2011.06.25
• 64 19

#### Abstract

Greg([Greg]) considered that $$N_k= \sum\limits_{i=1}^k(-1)^{i+1}P_{i,k}(p)N_1^i$$ where the $P_{i,k}$'s were polynomials with positive integer coefficients. In this paper, we will give the equations for $\sum\limits{P_{i,k}$ modulo 3. Using this, if we send a information for elliptic curve to sender, we can make a new checksum method for Manchester coding in IEEE 802.3 or IEEE 802.4.

#### Keywords

Congruences;Elliptic curve

#### References

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