MinT - Information on Result #2615029

Information on Result #2615029

Linear OOA(2¹⁸³, 69, F₂, 3, 100) (dual of [(69, 3), 24, 101]-NRT-code), using strength reduction based on linear OOA(2¹⁸³, 69, F₂, 3, 101) (dual of [(69, 3), 24, 102]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16¹⁷, 23, F₁₆, 16) (dual of [23, 6, 17]-code), using
  - discarding factors / shortening the dual code based on linear OA(16¹⁷, 24, F₁₆, 16) (dual of [24, 7, 17]-code), using
    - extended algebraic-geometric code AG_e(F,7P) [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(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(2¹⁸⁴, 69, F₂, 3, 100) (dual of [(69, 3), 23, 101]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹⁸², 68, F₂, 3, 99) (dual of [(68, 3), 22, 100]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(2¹⁸¹, 68, F₂, 3, 98) (dual of [(68, 3), 23, 99]-NRT-code)	[i]
4	Linear OOA(2¹⁸⁰, 68, F₂, 3, 97) (dual of [(68, 3), 24, 98]-NRT-code)	[i]
5	Linear OOA(2¹⁷⁹, 67, F₂, 3, 96) (dual of [(67, 3), 22, 97]-NRT-code)	[i]
6	Linear OOA(2¹⁷⁸, 67, F₂, 3, 95) (dual of [(67, 3), 23, 96]-NRT-code)	[i]
7	Linear OOA(2¹⁷⁷, 67, F₂, 3, 94) (dual of [(67, 3), 24, 95]-NRT-code)	[i]
8	Linear OOA(2¹⁷⁶, 66, F₂, 3, 93) (dual of [(66, 3), 22, 94]-NRT-code)	[i]
9	Linear OOA(2¹⁷⁵, 66, F₂, 3, 92) (dual of [(66, 3), 23, 93]-NRT-code)	[i]
10	Linear OOA(2¹⁷³, 65, F₂, 3, 90) (dual of [(65, 3), 22, 91]-NRT-code)	[i]