MinT - Information on Result #2673341

Information on Result #2673341

Linear OOA(2¹⁵³, 56, F₂, 3, 88) (dual of [(56, 3), 15, 89]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2¹⁵⁰, 55, F₂, 3, 88) (dual of [(55, 3), 15, 89]-NRT-code), using

strength reduction [i] based on linear OOA(2¹⁵⁰, 55, F₂, 3, 89) (dual of [(55, 3), 15, 90]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OA(32⁸, 11, F₃₂, 8) (dual of [11, 3, 9]-code or 11-arc in PG(7,32)), using
    - discarding factors / shortening the dual code based on linear OA(32⁸, 32, F₃₂, 8) (dual of [32, 24, 9]-code or 32-arc in PG(7,32)), using
      - Reedâ€“Solomon code RS(24,32) [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(2¹⁵³, 28, F₂, 6, 88) (dual of [(28, 6), 15, 89]-NRT-code)	[i]		OOA Folding