MinT - Information on Result #941539

Information on Result #941539

Linear OOA(2²⁰⁵, 106, F₂, 2, 122) (dual of [(106, 2), 7, 123]-NRT-code), using juxtaposition based on

linear OOA(2³⁹, 23, F₂, 2, 23) (dual of [(23, 2), 7, 24]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2³⁹, 24, F₂, 2, 23) (dual of [(24, 2), 9, 24]-NRT-code), using
  - concatenation of two NRT-codes [i] based on
    1. linear OA(8⁵, 8, F₈, 5) (dual of [8, 3, 6]-code or 8-arc in PG(4,8)), using
      - Reedâ€“Solomon code RS(3,8) [i]
    2. linear OOA(2³, 3, F₂, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;3,2) [i]
linear OOA(2¹⁵⁹, 83, F₂, 2, 98) (dual of [(83, 2), 7, 99]-NRT-code), using
- 1 step truncation [i] based on linear OOA(2¹⁶⁰, 84, F₂, 2, 99) (dual of [(84, 2), 8, 100]-NRT-code), using
  - concatenation of two NRT-codes [i] based on
    1. linear OA(4²⁴, 28, F₄, 19) (dual of [28, 4, 20]-code), using
      - an explicit generator matrix [i]
    2. linear OOA(2⁴, 3, F₂, 2, 4) (dual of [(3, 2), 2, 5]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;2,2) [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(2²⁰⁵, 106, F₂, 2, 121) (dual of [(106, 2), 7, 122]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2²⁰⁵, 106, F₂, 2, 120) (dual of [(106, 2), 7, 121]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(2²⁰⁵, 53, F₂, 4, 122) (dual of [(53, 4), 7, 123]-NRT-code)	[i]		OOA Folding