MinT - Information on Result #2795690

Information on Result #2795690

Linear OOA(2²⁵⁶, 82, F₂, 4, 110) (dual of [(82, 4), 72, 111]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2²⁵², 81, F₂, 4, 110) (dual of [(81, 4), 72, 111]-NRT-code), using

strength reduction [i] based on linear OOA(2²⁵², 81, F₂, 4, 111) (dual of [(81, 4), 72, 112]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OA(64¹⁵, 27, F₆₄, 15) (dual of [27, 12, 16]-code or 27-arc in PG(14,64)), using
    - discarding factors / shortening the dual code based on linear OA(64¹⁵, 64, F₆₄, 15) (dual of [64, 49, 16]-code or 64-arc in PG(14,64)), using
      - Reedâ€“Solomon code RS(49,64) [i]
  2. linear OOA(2⁶, 3, F₂, 4, 6) (dual of [(3, 4), 6, 7]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(4;6,2) [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(2²⁵⁶, 41, F₂, 7, 110) (dual of [(41, 7), 31, 111]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²⁵⁶, 41, F₂, 8, 110) (dual of [(41, 8), 72, 111]-NRT-code)	[i]		OOA Folding