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Polynomials

Polynomials used for error correction, signature analysis and generating pseudo random numbers.

  Degree  

  Polynomial  

  Remarks  

2

x2+x+1

 

3

x3+x+1

 

4

x4+x+1

 

5

x5+x2+1

 

6

x6+x+1

 

7

x7+x3+1

 

8

x8+x6+x5+x3+1

 

8

x8+x2+x+1

ATM

9

x9+x4+x1

 

10

x10+x3+1

 

10

x10+x9+x5+x4+x+1

ATM  

11

x11+x2+1

 

12

x12+x11+x3+x2+1

 

12

x12+x6+x4+x+1

 

13

x13+x4+x3+x+1

 

14

x14+x10+x6+x+1

 

15

x15+x+1

 

16

x16+x12+x3+x+1

 

16

x16+x12+x5+1

CCITT  

16

x16+x15+x2+1

 

16

x16+x15+x5+1

ANSI

17

x17+x3+1

 

18

x18+x7+x+1

 

19

x19+x5+x2+x+1

 

20

x20+x3+1

 

32

x32+x26+x23+x16+x12+x11+x10+x8+x7+x5+x4+x2+x+1

Ethernet,

Token Ring

FDDI networks

 

See books on computer codes. Click here for UK or here for USA.

See books on communication codes. Click here for UK or here for USA.

To see equation polynminial x^7 + x^3 +1 implemented in a hardware circuit click here.

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(c) Compiled by B V Wood.

 

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