MinT - Information on Result #1042403

Information on Result #1042403

Linear OOA(8¹⁶⁸, 109, F₈, 3, 113) (dual of [(109, 3), 159, 114]-NRT-code), using constructionÂ X applied to AG(3;F,177P) âŠ‚ AG(3;F,195P) based on

linear OOA(8¹⁵⁰, 97, F₈, 3, 113) (dual of [(97, 3), 141, 114]-NRT-code), using algebraic-geometric NRT-code AG(3;F,177P) [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
- F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]
linear OOA(8¹³², 97, F₈, 3, 95) (dual of [(97, 3), 159, 96]-NRT-code), using algebraic-geometric NRT-code AG(3;F,195P) [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98 (see above)
linear OOA(8¹⁸, 12, F₈, 3, 17) (dual of [(12, 3), 18, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8¹⁸, 14, F₈, 3, 17) (dual of [(14, 3), 24, 18]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,24P) [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]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(8¹⁶⁸, 109, F₈, 3, 112) (dual of [(109, 3), 159, 113]-NRT-code)	[i]		Strength Reduction for OOAs