MinT - Information on Result #924332

Information on Result #924332

Linear OOA(8¹³⁰, 110, F₈, 2, 80) (dual of [(110, 2), 90, 81]-NRT-code), using constructionÂ X applied to AG(2;F,113P) âŠ‚ AG(2;F,126P) based on

linear OOA(8¹¹⁷, 97, F₈, 2, 80) (dual of [(97, 2), 77, 81]-NRT-code), using algebraic-geometric NRT-code AG(2;F,113P) [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(8¹⁰⁴, 97, F₈, 2, 67) (dual of [(97, 2), 90, 68]-NRT-code), using algebraic-geometric NRT-code AG(2;F,126P) [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98 (see above)
linear OOA(8¹³, 13, F₈, 2, 12) (dual of [(13, 2), 13, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8¹³, 14, F₈, 2, 12) (dual of [(14, 2), 15, 13]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,15P) [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(8¹³⁰, 55, F₈, 3, 80) (dual of [(55, 3), 35, 81]-NRT-code)	[i]		OOA Folding