MinT - Information on Result #1027748

Information on Result #1027748

Linear OOA(8¹⁷³, 59, F₈, 3, 160) (dual of [(59, 3), 4, 161]-NRT-code), using juxtaposition based on

linear OOA(8²⁹, 11, F₈, 3, 28) (dual of [(11, 3), 4, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8²⁹, 14, F₈, 3, 28) (dual of [(14, 3), 13, 29]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,13P) [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(8¹⁴⁰, 48, F₈, 3, 131) (dual of [(48, 3), 4, 132]-NRT-code), using
- repeating each code word 2 times [i] based on linear OOA(8⁶⁸, 24, F₈, 3, 65) (dual of [(24, 3), 4, 66]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,6P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
    - the Klein quartic over F₈ [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(8¹⁶², 55, F₈, 3, 149) (dual of [(55, 3), 3, 150]-NRT-code)	[i]		Truncation for OOAs