| 41. | Fix a finite field GF ( q ), where q is a prime power.
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| 42. | In particular, this applies to finite field extensions of " K ".
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| 43. | And we consider this as defining an algebraic curve over the finite field with elements.
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| 44. | Both of these approaches may evaluate the elements of the finite field in any order.
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| 45. | Every finite field is a simple extension of the prime field of the same characteristic.
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| 46. | Dowling lattice of the multiplicative group of a finite field " F ".
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| 47. | This is because addition in any characteristic two finite field reduces to the XOR operation.
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| 48. | The non-zero elements of a finite field form a cyclic group under multiplication.
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| 49. | Every hyperfinite field is pseudo-finite and every pseudo-finite field is quasifinite.
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| 50. | The number of elements of a finite field is called its " order ".
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