MinT - Information on Result #1026793

Information on Result #1026793

Linear OOA(4²⁴¹, 87, F₄, 3, 174) (dual of [(87, 3), 20, 175]-NRT-code), using juxtaposition based on

linear OOA(4⁷³, 31, F₄, 3, 58) (dual of [(31, 3), 20, 59]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4⁷³, 32, F₄, 3, 58) (dual of [(32, 3), 23, 59]-NRT-code), using
  - algebraic-geometric NRT-code AG(3;F,37P) [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]
linear OOA(4¹⁴⁸, 56, F₄, 3, 115) (dual of [(56, 3), 20, 116]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,52P) [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
  - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4²⁴¹, 87, F₄, 3, 173) (dual of [(87, 3), 20, 174]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(4²⁴¹, 87, F₄, 3, 172) (dual of [(87, 3), 20, 173]-NRT-code)	[i]		Strength Reduction for OOAs