MinT - Information on Result #2612174

Information on Result #2612174

Linear OOA(2¹²⁷, 45, F₂, 3, 85) (dual of [(45, 3), 8, 86]-NRT-code), using strength reduction based on linear OOA(2¹²⁷, 45, F₂, 3, 87) (dual of [(45, 3), 8, 88]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16⁷, 9, F₁₆, 7) (dual of [9, 2, 8]-code or 9-arc in PG(6,16)), using
  - discarding factors / shortening the dual code based on linear OA(16⁷, 16, F₁₆, 7) (dual of [16, 9, 8]-code or 16-arc in PG(6,16)), using
    - Reedâ€“Solomon code RS(9,16) [i]
2. linear OOA(2¹¹, 5, F₂, 3, 10) (dual of [(5, 3), 4, 11]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;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(2¹²⁸, 45, F₂, 3, 85) (dual of [(45, 3), 7, 86]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹²⁶, 44, F₂, 3, 84) (dual of [(44, 3), 6, 85]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(2¹²⁵, 44, F₂, 3, 83) (dual of [(44, 3), 7, 84]-NRT-code)	[i]
4	Linear OOA(2¹²⁴, 44, F₂, 3, 82) (dual of [(44, 3), 8, 83]-NRT-code)	[i]
5	Linear OOA(2¹²³, 43, F₂, 3, 81) (dual of [(43, 3), 6, 82]-NRT-code)	[i]
6	Linear OOA(2¹²², 43, F₂, 3, 80) (dual of [(43, 3), 7, 81]-NRT-code)	[i]
7	Linear OOA(2¹²¹, 43, F₂, 3, 79) (dual of [(43, 3), 8, 80]-NRT-code)	[i]
8	Linear OOA(2¹¹⁹, 42, F₂, 3, 77) (dual of [(42, 3), 7, 78]-NRT-code)	[i]