MinT - Information on Result #905576

Information on Result #905576

Linear OOA(256⁴⁰, 4324863, F₂₅₆, 2, 10) (dual of [(4324863, 2), 8649686, 11]-NRT-code), using (u,Â u+v)-construction 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]
linear OOA(256²⁸, 4194301, F₂₅₆, 2, 10) (dual of [(4194301, 2), 8388574, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(256²⁸, 8388602, F₂₅₆, 10) (dual of [8388602, 8388574, 11]-code), using
  - discarding factors / shortening the dual code based on linear OA(256²⁸, large, F₂₅₆, 10) (dual of [large, large−28, 11]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m 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, 2162431, F₂₅₆, 4, 10) (dual of [(2162431, 4), 8649684, 11]-NRT-code)	[i]		OOA Folding