MinT - Information on Result #904334

Information on Result #904334

Linear OOA(81⁵⁰, 4197623, F₈₁, 2, 11) (dual of [(4197623, 2), 8395196, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(81⁹, 3322, F₈₁, 2, 5) (dual of [(3322, 2), 6635, 6]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(81², 82, F₈₁, 2, 2) (dual of [(82, 2), 162, 3]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;162,81) [i]
  2. linear OOA(81⁷, 3240, F₈₁, 2, 5) (dual of [(3240, 2), 6473, 6]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(81⁷, 6480, F₈₁, 5) (dual of [6480, 6473, 6]-code), using
      - discarding factors / shortening the dual code based on 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.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(81⁵⁰, 2098811, F₈₁, 4, 11) (dual of [(2098811, 4), 8395194, 12]-NRT-code)	[i]		OOA Folding