MinT - Information on Result #910456

Information on Result #910456

Linear OOA(8¹⁷³, 89, F₈, 2, 154) (dual of [(89, 2), 5, 155]-NRT-code), using juxtaposition based on

linear OOA(8¹⁹, 12, F₈, 2, 18) (dual of [(12, 2), 5, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8¹⁹, 14, F₈, 2, 18) (dual of [(14, 2), 9, 19]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,9P) [i] based on function field F/F₈ with g(F) = 1 and N(F) ≥ 14, using
    - F₂ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]
linear OOA(8¹⁴⁹, 77, F₈, 2, 135) (dual of [(77, 2), 5, 136]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(8¹⁹, 12, F₈, 2, 18) (dual of [(12, 2), 5, 19]-NRT-code) (see above)
  2. linear OOA(8¹²⁵, 65, F₈, 2, 116) (dual of [(65, 2), 5, 117]-NRT-code), using
    - standard lengthening with (d₀,â€¦,d₁)Â = (115,116) [i] based on linear OOA(8¹²³, 64, F₈, 2, 114) (dual of [(64, 2), 5, 115]-NRT-code), using algebraic-geometric NRT-code AG(2;F,13P) with known gap numbers [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using the Suzuki function field over F₈ [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(8¹⁷³, 89, F₈, 2, 153) (dual of [(89, 2), 5, 154]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(8¹⁷³, 89, F₈, 2, 152) (dual of [(89, 2), 5, 153]-NRT-code)	[i]		Strength Reduction for OOAs