MinT - Information on Result #2843665

Information on Result #2843665

Linear OOA(2¹⁹⁴, 52, F₂, 5, 114) (dual of [(52, 5), 66, 115]-NRT-code), using strength reduction based on linear OOA(2¹⁹⁴, 52, F₂, 5, 115) (dual of [(52, 5), 66, 116]-NRT-code), using

constructionÂ X applied to AG(5;F,62P) âŠ‚ AG(5;F,67P) [i] based on
1. linear OOA(2¹⁸⁴, 48, F₂, 5, 115) (dual of [(48, 5), 56, 116]-NRT-code), using algebraic-geometric NRT-code AG(5;F,62P) with degPÂ =Â 2 [i] based on function field F/F₂ with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
2. linear OOA(2¹⁷⁴, 48, F₂, 5, 105) (dual of [(48, 5), 66, 106]-NRT-code), using algebraic-geometric NRT-code AG(5;F,67P) with degPÂ =Â 2 [i] based on function field F/F₂ with g(F) = 69 and N(F) ≥ 48 (see above)
3. linear OOA(2¹⁰, 4, F₂, 5, 9) (dual of [(4, 5), 10, 10]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(2¹⁰, 5, F₂, 4, 9) (dual of [(5, 4), 10, 10]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,10P) [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.

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(2¹⁹⁵, 52, F₂, 5, 114) (dual of [(52, 5), 65, 115]-NRT-code)	[i]		OOA Duplication