MinT - Information on Result #2611286

Information on Result #2611286

Linear OOA(2¹⁰², 36, F₂, 3, 70) (dual of [(36, 3), 6, 71]-NRT-code), using strength reduction based on linear OOA(2¹⁰², 36, F₂, 3, 71) (dual of [(36, 3), 6, 72]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(8⁷, 9, F₈, 7) (dual of [9, 2, 8]-code or 9-arc in PG(6,8)), using
  - extended Reedâ€“Solomon code RS_e(2,8) [i]
  - Simplex code S(2,8) [i]
2. linear OOA(2⁹, 4, F₂, 3, 8) (dual of [(4, 3), 3, 9]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(2⁹, 5, F₂, 3, 8) (dual of [(5, 3), 6, 9]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,6P) [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(2¹⁰², 18, F₂, 6, 70) (dual of [(18, 6), 6, 71]-NRT-code)	[i]		OOA Folding