MinT - Information on Result #2618537

Information on Result #2618537

Linear OOA(2²³⁸, 90, F₂, 3, 124) (dual of [(90, 3), 32, 125]-NRT-code), using strength reduction based on linear OOA(2²³⁸, 90, F₂, 3, 125) (dual of [(90, 3), 32, 126]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16²², 30, F₁₆, 20) (dual of [30, 8, 21]-code), using
  - discarding factors / shortening the dual code based on linear OA(16²², 33, F₁₆, 20) (dual of [33, 11, 21]-code), using
    - extended algebraic-geometric code AG_e(F,12P) [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
      - a function field by SÃ©mirat [i]
2. linear OOA(2⁵, 3, F₂, 3, 5) (dual of [(3, 3), 4, 6]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(3;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		Method
1	Linear OOA(2²³⁹, 90, F₂, 3, 124) (dual of [(90, 3), 31, 125]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²³⁷, 89, F₂, 3, 123) (dual of [(89, 3), 30, 124]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(2²³⁶, 89, F₂, 3, 122) (dual of [(89, 3), 31, 123]-NRT-code)	[i]
4	Linear OOA(2²³⁵, 89, F₂, 3, 121) (dual of [(89, 3), 32, 122]-NRT-code)	[i]
5	Linear OOA(2²³⁴, 88, F₂, 3, 120) (dual of [(88, 3), 30, 121]-NRT-code)	[i]
6	Linear OOA(2²³³, 88, F₂, 3, 119) (dual of [(88, 3), 31, 120]-NRT-code)	[i]
7	Linear OOA(2²³², 88, F₂, 3, 118) (dual of [(88, 3), 32, 119]-NRT-code)	[i]
8	Linear OOA(2²³¹, 87, F₂, 3, 117) (dual of [(87, 3), 30, 118]-NRT-code)	[i]
9	Linear OOA(2²³⁰, 87, F₂, 3, 116) (dual of [(87, 3), 31, 117]-NRT-code)	[i]
10	Linear OOA(2²³⁸, 45, F₂, 6, 124) (dual of [(45, 6), 32, 125]-NRT-code)	[i]	OOA Folding