MinT - Information on Result #1042434

Information on Result #1042434

Linear OOA(8¹³⁷, 109, F₈, 3, 82) (dual of [(109, 3), 190, 83]-NRT-code), using constructionÂ X applied to AG(3;F,208P) âŠ‚ AG(3;F,226P) based on

linear OOA(8¹¹⁹, 97, F₈, 3, 82) (dual of [(97, 3), 172, 83]-NRT-code), using algebraic-geometric NRT-code AG(3;F,208P) [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(8¹⁰¹, 97, F₈, 3, 64) (dual of [(97, 3), 190, 65]-NRT-code), using algebraic-geometric NRT-code AG(3;F,226P) [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(8¹³⁷, 109, F₈, 3, 81) (dual of [(109, 3), 190, 82]-NRT-code)	[i]		Strength Reduction for OOAs