MinT - Information on Result #2441153

Information on Result #2441153

Linear OOA(4¹⁶⁴, 90, F₄, 2, 110) (dual of [(90, 2), 16, 111]-NRT-code), using strength reduction based on linear OOA(4¹⁶⁴, 90, F₄, 2, 111) (dual of [(90, 2), 16, 112]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(16²⁸, 18, F₁₆, 2, 27) (dual of [(18, 2), 8, 28]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(16²⁸, 24, F₁₆, 2, 27) (dual of [(24, 2), 20, 28]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,20P) [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, using
      - a function field by SÃ©mirat [i]
2. linear OA(4³, 5, F₄, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,4) or 5-cap in PG(2,4)), using
  - extended Reedâ€“Solomon code RS_e(2,4) [i]
  - Simplex code S(2,4) [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		Method
1	Linear OOA(4¹⁶³, 89, F₄, 2, 109) (dual of [(89, 2), 15, 110]-NRT-code)	[i]	Truncation for OOAs
2	Linear OOA(4¹⁶², 89, F₄, 2, 108) (dual of [(89, 2), 16, 109]-NRT-code)	[i]
3	Linear OOA(4¹⁵⁹, 87, F₄, 2, 105) (dual of [(87, 2), 15, 106]-NRT-code)	[i]