MinT - Information on Result #2619416

Information on Result #2619416

Linear OOA(2²⁵⁰, 90, F₂, 3, 144) (dual of [(90, 3), 20, 145]-NRT-code), using strength reduction based on linear OOA(2²⁵⁰, 90, F₂, 3, 149) (dual of [(90, 3), 20, 150]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(32¹⁴, 18, F₃₂, 14) (dual of [18, 4, 15]-code or 18-arc in PG(13,32)), using
  - discarding factors / shortening the dual code based on linear OA(32¹⁴, 32, F₃₂, 14) (dual of [32, 18, 15]-code or 32-arc in PG(13,32)), using
    - Reedâ€“Solomon code RS(18,32) [i]
2. linear OOA(2¹⁰, 5, F₂, 3, 9) (dual of [(5, 3), 5, 10]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,5P) [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(2²⁵¹, 90, F₂, 3, 144) (dual of [(90, 3), 19, 145]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²⁵², 90, F₂, 3, 144) (dual of [(90, 3), 18, 145]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁴⁹, 89, F₂, 3, 143) (dual of [(89, 3), 18, 144]-NRT-code)	[i]	Truncation for OOAs
4	Linear OOA(2²⁴⁸, 89, F₂, 3, 142) (dual of [(89, 3), 19, 143]-NRT-code)	[i]
5	Linear OOA(2²⁴⁷, 89, F₂, 3, 141) (dual of [(89, 3), 20, 142]-NRT-code)	[i]
6	Linear OOA(2²⁴⁶, 88, F₂, 3, 140) (dual of [(88, 3), 18, 141]-NRT-code)	[i]
7	Linear OOA(2²⁵⁰, 45, F₂, 6, 144) (dual of [(45, 6), 20, 145]-NRT-code)	[i]	OOA Folding