MinT - Information on Result #2768385

Information on Result #2768385

Linear OOA(2²⁶⁰, 70, F₂, 4, 158) (dual of [(70, 4), 20, 159]-NRT-code), using strength reduction based on linear OOA(2²⁶⁰, 70, F₂, 4, 164) (dual of [(70, 4), 20, 165]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(32¹⁰, 14, F₃₂, 10) (dual of [14, 4, 11]-code or 14-arc in PG(9,32)), using
  - discarding factors / shortening the dual code based on linear OA(32¹⁰, 32, F₃₂, 10) (dual of [32, 22, 11]-code or 32-arc in PG(9,32)), using
    - Reedâ€“Solomon code RS(22,32) [i]
2. linear OOA(2¹⁵, 5, F₂, 4, 14) (dual of [(5, 4), 5, 15]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;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(2²⁵⁹, 69, F₂, 4, 157) (dual of [(69, 4), 17, 158]-NRT-code)	[i]	Truncation for OOAs
2	Linear OOA(2²⁵⁸, 69, F₂, 4, 156) (dual of [(69, 4), 18, 157]-NRT-code)	[i]
3	Linear OOA(2²⁵⁷, 69, F₂, 4, 155) (dual of [(69, 4), 19, 156]-NRT-code)	[i]
4	Linear OOA(2²⁵⁵, 68, F₂, 4, 153) (dual of [(68, 4), 17, 154]-NRT-code)	[i]
5	Linear OOA(2²⁶⁰, 35, F₂, 8, 158) (dual of [(35, 8), 20, 159]-NRT-code)	[i]	OOA Folding