MinT - Information on Result #2765144

Information on Result #2765144

Linear OOA(2²¹², 57, F₂, 4, 133) (dual of [(57, 4), 16, 134]-NRT-code), using strength reduction based on linear OOA(2²¹², 57, F₂, 4, 134) (dual of [(57, 4), 16, 135]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16¹⁵, 19, F₁₆, 14) (dual of [19, 4, 15]-code), using
  - discarding factors / shortening the dual code based on linear OA(16¹⁵, 24, F₁₆, 14) (dual of [24, 9, 15]-code), using
    - extended algebraic-geometric code AG_e(F,9P) [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 OOA(2⁸, 3, F₂, 4, 8) (dual of [(3, 4), 4, 9]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(4;4,2) [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(2²⁰⁹, 56, F₂, 4, 130) (dual of [(56, 4), 15, 131]-NRT-code)	[i]		Truncation for OOAs
2	Linear OOA(2²⁰⁴, 55, F₂, 4, 125) (dual of [(55, 4), 16, 126]-NRT-code)	[i]		Truncation for OOAs