MinT - Information on Result #1129537

Information on Result #1129537

Linear OOA(2²⁵⁵, 79, F₂, 5, 100) (dual of [(79, 5), 140, 101]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁹⁶, 35, F₂, 5, 50) (dual of [(35, 5), 79, 51]-NRT-code), using
- constructionÂ X applied to AG(5;F,109P) âŠ‚ AG(5;F,117P) [i] based on
  1. linear OOA(2⁸⁹, 32, F₂, 5, 50) (dual of [(32, 5), 71, 51]-NRT-code), using algebraic-geometric NRT-code AG(5;F,109P) [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]
  2. linear OOA(2⁸¹, 32, F₂, 5, 42) (dual of [(32, 5), 79, 43]-NRT-code), using algebraic-geometric NRT-code AG(5;F,117P) [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33 (see above)
  3. linear OOA(2⁷, 3, F₂, 5, 7) (dual of [(3, 5), 8, 8]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(5;8,2) [i]
linear OOA(2¹⁵⁹, 44, F₂, 5, 100) (dual of [(44, 5), 61, 101]-NRT-code), using
- constructionÂ X applied to AG(5;F,18P) âŠ‚ AG(5;F,19P) [i] based on
  1. linear OOA(2¹⁵⁵, 42, F₂, 5, 101) (dual of [(42, 5), 55, 102]-NRT-code), using algebraic-geometric NRT-code AG(5;F,18P) 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(2¹⁴⁹, 42, F₂, 5, 95) (dual of [(42, 5), 61, 96]-NRT-code), using algebraic-geometric NRT-code AG(5;F,19P) with degPÂ =Â 6 [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42 (see above)
  3. linear OOA(2⁴, 2, F₂, 5, 4) (dual of [(2, 5), 6, 5]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(5;6,2) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²⁵⁵, 79, F₂, 5, 99) (dual of [(79, 5), 140, 100]-NRT-code)	[i]		Strength Reduction for OOAs