MinT - Information on Result #2483749

Information on Result #2483749

Linear OOA(2²⁴², 136, F₂, 2, 108) (dual of [(136, 2), 30, 109]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2²⁴⁰, 135, F₂, 2, 108) (dual of [(135, 2), 30, 109]-NRT-code), using

strength reduction [i] based on linear OOA(2²⁴⁰, 135, F₂, 2, 109) (dual of [(135, 2), 30, 110]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OA(32²¹, 27, F₃₂, 21) (dual of [27, 6, 22]-code or 27-arc in PG(20,32)), using
    - discarding factors / shortening the dual code based on linear OA(32²¹, 32, F₃₂, 21) (dual of [32, 11, 22]-code or 32-arc in PG(20,32)), using
      - Reedâ€“Solomon code RS(11,32) [i]
  2. linear OOA(2⁵, 5, F₂, 2, 4) (dual of [(5, 2), 5, 5]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;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(2²⁴², 68, F₂, 4, 108) (dual of [(68, 4), 30, 109]-NRT-code)	[i]		OOA Folding