MinT - Information on Result #2761043

Information on Result #2761043

Linear OOA(2¹⁴², 37, F₂, 4, 107) (dual of [(37, 4), 6, 108]-NRT-code), using strength reduction based on linear OOA(2¹⁴², 37, F₂, 4, 108) (dual of [(37, 4), 6, 109]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2³⁴, 10, F₂, 4, 28) (dual of [(10, 4), 6, 29]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,11P) [i] based on function field F/F₂ with g(F) = 6 and N(F) ≥ 10, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(2¹⁰², 27, F₂, 4, 79) (dual of [(27, 4), 6, 80]-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, 3, F₂, 4, 9) (dual of [(3, 4), 3, 10]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(4;3,2) [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(2¹³², 34, F₂, 4, 97) (dual of [(34, 4), 4, 98]-NRT-code)	[i]		Truncation for OOAs