MinT - Information on Result #2471244

Information on Result #2471244

Linear OOA(4²⁰⁵, 109, F₄, 2, 145) (dual of [(109, 2), 13, 146]-NRT-code), using 1 step truncation based on linear OOA(4²⁰⁶, 110, F₄, 2, 146) (dual of [(110, 2), 14, 147]-NRT-code), using

strength reduction [i] based on linear OOA(4²⁰⁶, 110, F₄, 2, 147) (dual of [(110, 2), 14, 148]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OOA(16³⁷, 22, F₁₆, 2, 36) (dual of [(22, 2), 7, 37]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(16³⁷, 24, F₁₆, 2, 36) (dual of [(24, 2), 11, 37]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,11P) [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		This result only	Method
1	Linear OOA(4²²³, 116, F₄, 2, 154) (dual of [(116, 2), 9, 155]-NRT-code)	[i]		Juxtaposition for OOAs