MinT - Information on Result #910455

Information on Result #910455

Linear OOA(8¹⁶⁷, 86, F₈, 2, 149) (dual of [(86, 2), 5, 150]-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(8¹⁴³, 74, F₈, 2, 130) (dual of [(74, 2), 5, 131]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(8¹³, 9, F₈, 2, 13) (dual of [(9, 2), 5, 14]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;5,8) [i]
  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(8¹⁶⁷, 86, F₈, 2, 148) (dual of [(86, 2), 5, 149]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(8¹⁶⁷, 86, F₈, 2, 147) (dual of [(86, 2), 5, 148]-NRT-code)	[i]		Strength Reduction for OOAs