MinT - Information on Result #1149856

Information on Result #1149856

Linear OOA(2²²⁹, 79, F₂, 6, 83) (dual of [(79, 6), 245, 84]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁸⁰, 33, F₂, 6, 41) (dual of [(33, 6), 118, 42]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(6;F,156P) [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33, using
  - an explicitly constructive algebraic function field [i]
linear OOA(2¹⁴⁹, 46, F₂, 6, 83) (dual of [(46, 6), 127, 84]-NRT-code), using
- constructionÂ X applied to AG(6;F,28P) âŠ‚ AG(6;F,30P) [i] based on
  1. linear OOA(2¹³⁷, 42, F₂, 6, 83) (dual of [(42, 6), 115, 84]-NRT-code), using algebraic-geometric NRT-code AG(6;F,28P) with degPÂ =Â 6 [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
  2. linear OOA(2¹²⁵, 42, F₂, 6, 71) (dual of [(42, 6), 127, 72]-NRT-code), using algebraic-geometric NRT-code AG(6;F,30P) with degPÂ =Â 6 [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42 (see above)
  3. linear OOA(2¹², 4, F₂, 6, 11) (dual of [(4, 6), 12, 12]-NRT-code), using
    - OOA stacking with additional row [i] based on linear OOA(2¹², 5, F₂, 5, 11) (dual of [(5, 5), 13, 12]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(5;F,13P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
        an explicitly constructive algebraic function field [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²³⁰, 79, F₂, 6, 83) (dual of [(79, 6), 244, 84]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2²³¹, 79, F₂, 6, 83) (dual of [(79, 6), 243, 84]-NRT-code)	[i]		OOA Duplication