MinT - Information on Result #904337

Information on Result #904337

Linear OOA(81⁵³, 4207263, F₈₁, 2, 11) (dual of [(4207263, 2), 8414473, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(81¹², 12962, F₈₁, 2, 5) (dual of [(12962, 2), 25912, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(81¹², 25924, F₈₁, 5) (dual of [25924, 25912, 6]-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OA(81¹, 6481, F₈₁, 1) (dual of [6481, 6480, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(81¹, s, F₈₁, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
    2. linear OA(81¹, 6481, F₈₁, 1) (dual of [6481, 6480, 2]-code) (see above)
    3. linear OA(81³, 6481, F₈₁, 2) (dual of [6481, 6478, 3]-code), using
      - discarding factors / shortening the dual code based on linear OA(81³, 6643, F₈₁, 2) (dual of [6643, 6640, 3]-code), using
        Hamming code H(3,81) [i]
    4. linear OA(81⁷, 6481, F₈₁, 5) (dual of [6481, 6474, 6]-code), using
      - a code by Danev and Olsson [i]
linear OOA(81⁴¹, 4194301, F₈₁, 2, 11) (dual of [(4194301, 2), 8388561, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(81⁴¹, 8388602, F₈₁, 11) (dual of [8388602, 8388561, 12]-code), using
  - discarding factors / shortening the dual code based on linear OA(81⁴¹, large, F₈₁, 11) (dual of [large, large−41, 12]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [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(81⁵³, 2103631, F₈₁, 4, 11) (dual of [(2103631, 4), 8414471, 12]-NRT-code)	[i]		OOA Folding