MinT - Information on Result #2418207

Information on Result #2418207

Linear OOA(2⁹⁸, 55, F₂, 2, 52) (dual of [(55, 2), 12, 53]-NRT-code), using strength reduction based on linear OOA(2⁹⁸, 55, F₂, 2, 53) (dual of [(55, 2), 12, 54]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16⁸, 11, F₁₆, 8) (dual of [11, 3, 9]-code or 11-arc in PG(7,16)), using
  - discarding factors / shortening the dual code based on linear OA(16⁸, 16, F₁₆, 8) (dual of [16, 8, 9]-code or 16-arc in PG(7,16)), using
    - Reedâ€“Solomon code RS(8,16) [i]
2. linear OOA(2⁶, 5, F₂, 2, 5) (dual of [(5, 2), 4, 6]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;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(2⁹⁷, 54, F₂, 2, 51) (dual of [(54, 2), 11, 52]-NRT-code)	[i]	Truncation for OOAs
2	Linear OOA(2⁹⁵, 53, F₂, 2, 49) (dual of [(53, 2), 11, 50]-NRT-code)	[i]
3	Linear OOA(2⁹⁴, 53, F₂, 2, 48) (dual of [(53, 2), 12, 49]-NRT-code)	[i]