MinT - Information on Result #2619790

Information on Result #2619790

Linear OOA(2²⁵⁵, 90, F₂, 3, 156) (dual of [(90, 3), 15, 157]-NRT-code), using strength reduction based on linear OOA(2²⁵⁵, 90, F₂, 3, 159) (dual of [(90, 3), 15, 160]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(32¹⁵, 18, F₃₂, 15) (dual of [18, 3, 16]-code or 18-arc in PG(14,32)), using
  - discarding factors / shortening the dual code based on linear OA(32¹⁵, 32, F₃₂, 15) (dual of [32, 17, 16]-code or 32-arc in PG(14,32)), using
    - Reedâ€“Solomon code RS(17,32) [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(2²⁵⁶, 90, F₂, 3, 156) (dual of [(90, 3), 14, 157]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²⁵⁷, 90, F₂, 3, 156) (dual of [(90, 3), 13, 157]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁵⁵, 45, F₂, 6, 156) (dual of [(45, 6), 15, 157]-NRT-code)	[i]	OOA Folding