MinT - Information on Result #2610713

Information on Result #2610713

Linear OOA(2⁸⁴, 30, F₂, 3, 57) (dual of [(30, 3), 6, 58]-NRT-code), using strength reduction based on linear OOA(2⁸⁴, 30, F₂, 3, 59) (dual of [(30, 3), 6, 60]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(8⁴, 6, F₈, 4) (dual of [6, 2, 5]-code or 6-arc in PG(3,8)), using
  - discarding factors / shortening the dual code based on linear OA(8⁴, 8, F₈, 4) (dual of [8, 4, 5]-code or 8-arc in PG(3,8)), using
    - Reedâ€“Solomon code RS(4,8) [i]
2. linear OOA(2¹², 5, F₂, 3, 11) (dual of [(5, 3), 3, 12]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,3P) [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		This result only	Method
1	Linear OOA(2⁸⁴, 15, F₂, 6, 57) (dual of [(15, 6), 6, 58]-NRT-code)	[i]		OOA Folding