MinT - Information on Result #2656782

Information on Result #2656782

Linear OOA(2²²⁷, 84, F₂, 3, 124) (dual of [(84, 3), 25, 125]-NRT-code), using 3 step truncation based on linear OOA(2²³⁰, 85, F₂, 3, 127) (dual of [(85, 3), 25, 128]-NRT-code), using

strength reduction [i] based on linear OOA(2²³⁰, 85, F₂, 3, 129) (dual of [(85, 3), 25, 130]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OA(32¹², 17, F₃₂, 12) (dual of [17, 5, 13]-code or 17-arc in PG(11,32)), using
    - discarding factors / shortening the dual code based on linear OA(32¹², 32, F₃₂, 12) (dual of [32, 20, 13]-code or 32-arc in PG(11,32)), using
      - Reedâ€“Solomon code RS(20,32) [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		This result only	Method
1	Linear OOA(2²⁵⁷, 89, F₂, 3, 139) (dual of [(89, 3), 10, 140]-NRT-code)	[i]		Juxtaposition for OOAs
2	Linear OOA(2²²⁷, 42, F₂, 6, 124) (dual of [(42, 6), 25, 125]-NRT-code)	[i]		OOA Folding