MinT - Information on Result #924190

Information on Result #924190

Linear OOA(8¹²⁷, 108, F₈, 2, 79) (dual of [(108, 2), 89, 80]-NRT-code), using constructionÂ X applied to AG(2;F,114P) âŠ‚ AG(2;F,125P) based on

linear OOA(8¹¹⁶, 97, F₈, 2, 79) (dual of [(97, 2), 78, 80]-NRT-code), using algebraic-geometric NRT-code AG(2;F,114P) [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(8¹⁰⁵, 97, F₈, 2, 68) (dual of [(97, 2), 89, 69]-NRT-code), using algebraic-geometric NRT-code AG(2;F,125P) [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98 (see above)
linear OOA(8¹¹, 11, F₈, 2, 10) (dual of [(11, 2), 11, 11]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8¹¹, 14, F₈, 2, 10) (dual of [(14, 2), 17, 11]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,17P) [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(8¹²⁷, 54, F₈, 3, 79) (dual of [(54, 3), 35, 80]-NRT-code)	[i]		OOA Folding