MinT - Information on Result #1130547

Information on Result #1130547

Linear OOA(256¹², 130561, F₂₅₆, 6, 5) (dual of [(130561, 6), 783354, 6]-NRT-code), using OOA stacking with additional row based on linear OOA(256¹², 130562, F₂₅₆, 2, 5) (dual of [(130562, 2), 261112, 6]-NRT-code), using

OOA 2-folding [i] based on linear OA(256¹², 261124, F₂₅₆, 5) (dual of [261124, 261112, 6]-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OA(256¹, 65281, F₂₅₆, 1) (dual of [65281, 65280, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(256¹, s, F₂₅₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
  2. linear OA(256¹, 65281, F₂₅₆, 1) (dual of [65281, 65280, 2]-code) (see above)
  3. linear OA(256³, 65281, F₂₅₆, 2) (dual of [65281, 65278, 3]-code), using
    - discarding factors / shortening the dual code based on linear OA(256³, 65793, F₂₅₆, 2) (dual of [65793, 65790, 3]-code), using
      - Hamming code H(3,256) [i]
  4. linear OA(256⁷, 65281, F₂₅₆, 5) (dual of [65281, 65274, 6]-code), using
    - a code by Danev and Olsson [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(256⁴⁰, 1808281, F₂₅₆, 6, 10) (dual of [(1808281, 6), 10849646, 11]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(256⁴³, 1808281, F₂₅₆, 6, 11) (dual of [(1808281, 6), 10849643, 12]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs