MinT - Information on Result #2782585

Information on Result #2782585

Linear OOA(2²¹⁴, 58, F₂, 4, 130) (dual of [(58, 4), 18, 131]-NRT-code), using 8 step truncation based on linear OOA(2²²², 60, F₂, 4, 138) (dual of [(60, 4), 18, 139]-NRT-code), using

strength reduction [i] based on linear OOA(2²²², 60, F₂, 4, 139) (dual of [(60, 4), 18, 140]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OA(64⁹, 12, F₆₄, 9) (dual of [12, 3, 10]-code or 12-arc in PG(8,64)), using
    - discarding factors / shortening the dual code based on linear OA(64⁹, 64, F₆₄, 9) (dual of [64, 55, 10]-code or 64-arc in PG(8,64)), using
      - Reedâ€“Solomon code RS(55,64) [i]
  2. linear OOA(2¹⁴, 5, F₂, 4, 13) (dual of [(5, 4), 6, 14]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,6P) [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(2²¹⁴, 29, F₂, 8, 130) (dual of [(29, 8), 18, 131]-NRT-code)	[i]		OOA Folding