MinT - Information on Result #910408

Information on Result #910408

Linear OOA(8¹⁶¹, 84, F₈, 2, 140) (dual of [(84, 2), 7, 141]-NRT-code), using juxtaposition based on

linear OOA(8³¹, 19, F₈, 2, 28) (dual of [(19, 2), 7, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8³¹, 24, F₈, 2, 28) (dual of [(24, 2), 17, 29]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,19P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
    - the Klein quartic over F₈ [i]
linear OOA(8¹²³, 65, F₈, 2, 111) (dual of [(65, 2), 7, 112]-NRT-code), using
- standard lengthening with (d₀,â€¦,d₁)Â = (110,111) [i] based on linear OOA(8¹²¹, 64, F₈, 2, 109) (dual of [(64, 2), 7, 110]-NRT-code), using algebraic-geometric NRT-code AG(2;F,18P) 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(8¹⁶¹, 84, F₈, 2, 139) (dual of [(84, 2), 7, 140]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(8¹⁶¹, 84, F₈, 2, 138) (dual of [(84, 2), 7, 139]-NRT-code)	[i]		Strength Reduction for OOAs