MinT - Information on Result #906413

Information on Result #906413

Linear OOA(5⁸⁶, 45, F₅, 2, 71) (dual of [(45, 2), 4, 72]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(5¹⁵, 9, F₅, 2, 14) (dual of [(9, 2), 3, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(5¹⁵, 10, F₅, 2, 14) (dual of [(10, 2), 5, 15]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,5P) [i] based on function field F/F₅ with g(F) = 1 and N(F) ≥ 10, using
    - an explicitly constructive algebraic function field [i]
linear OOA(5¹⁷, 9, F₅, 2, 17) (dual of [(9, 2), 1, 18]-NRT-code), using
- dual of repetition NRT-code with length 9 [i]
linear OOA(5¹⁸, 9, F₅, 2, 18) (dual of [(9, 2), 0, 19]-NRT-code), using
- complete OOA / dual of NRT-code with only one code word [i]
linear OOA(5¹⁸, 9, F₅, 2, 18) (dual of [(9, 2), 0, 19]-NRT-code) (see above)
linear OOA(5¹⁸, 9, F₅, 2, 18) (dual of [(9, 2), 0, 19]-NRT-code) (see above)

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(5⁸⁶, 45, F₅, 2, 70) (dual of [(45, 2), 4, 71]-NRT-code)	[i]		Strength Reduction for OOAs