MinT - Information on Result #2460053

Information on Result #2460053

Linear OOA(2²¹⁶, 118, F₂, 2, 108) (dual of [(118, 2), 20, 109]-NRT-code), using 4 step truncation based on linear OOA(2²²⁰, 120, F₂, 2, 112) (dual of [(120, 2), 20, 113]-NRT-code), using

strength reduction [i] based on linear OOA(2²²⁰, 120, F₂, 2, 113) (dual of [(120, 2), 20, 114]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OA(16¹⁹, 24, F₁₆, 18) (dual of [24, 5, 19]-code), using
    - extended algebraic-geometric code AG_e(F,5P) [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(2⁶, 5, F₂, 2, 5) (dual of [(5, 2), 4, 6]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,4P) [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		Method
1	Linear OOA(2²²², 121, F₂, 2, 108) (dual of [(121, 2), 20, 109]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²²⁴, 122, F₂, 2, 108) (dual of [(122, 2), 20, 109]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(2²¹⁶, 59, F₂, 4, 108) (dual of [(59, 4), 20, 109]-NRT-code)	[i]	OOA Folding