MinT - Information on Result #2760856

Information on Result #2760856

Linear OOA(2¹³⁸, 52, F₂, 4, 60) (dual of [(52, 4), 70, 61]-NRT-code), using strength reduction based on linear OOA(2¹³⁸, 52, F₂, 4, 61) (dual of [(52, 4), 70, 62]-NRT-code), using

constructionÂ X applied to AG(4;F,65P) âŠ‚ AG(4;F,69P) [i] based on
1. linear OOA(2¹³⁰, 48, F₂, 4, 61) (dual of [(48, 4), 62, 62]-NRT-code), using algebraic-geometric NRT-code AG(4;F,65P) 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(2¹²², 48, F₂, 4, 53) (dual of [(48, 4), 70, 54]-NRT-code), using algebraic-geometric NRT-code AG(4;F,69P) with degPÂ =Â 2 [i] based on function field F/F₂ with g(F) = 69 and N(F) ≥ 48 (see above)
3. linear OOA(2⁸, 4, F₂, 4, 7) (dual of [(4, 4), 8, 8]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(2⁸, 5, F₂, 3, 7) (dual of [(5, 3), 7, 8]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,7P) [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(2¹³⁸, 26, F₂, 7, 60) (dual of [(26, 7), 44, 61]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2¹³⁸, 26, F₂, 8, 60) (dual of [(26, 8), 70, 61]-NRT-code)	[i]		OOA Folding