MinT - Information on Result #1016055

Information on Result #1016055

Linear OOA(9⁹⁹, 5598973, F₉, 3, 11) (dual of [(5598973, 3), 16796820, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(9¹⁷, 6571, F₉, 3, 5) (dual of [(6571, 3), 19696, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(9¹⁷, 6572, F₉, 2, 5) (dual of [(6572, 2), 13127, 6]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(9³, 91, F₉, 2, 2) (dual of [(91, 2), 179, 3]-NRT-code), using
      - appending kth column [i] based on linear OA(9³, 91, F₉, 2) (dual of [91, 88, 3]-code), using
        Hamming code H(3,9) [i]
    2. linear OOA(9¹⁴, 6481, F₉, 2, 5) (dual of [(6481, 2), 12948, 6]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(9¹⁴, 12962, F₉, 5) (dual of [12962, 12948, 6]-code), using
        trace code [i] based on linear OA(81⁷, 6481, F₈₁, 5) (dual of [6481, 6474, 6]-code), using
        a code by Danev and Olsson [i]
linear OOA(9⁸², 5592402, F₉, 3, 11) (dual of [(5592402, 3), 16777124, 12]-NRT-code), using
- trace code [i] based on linear OOA(81⁴¹, 2796201, F₈₁, 3, 11) (dual of [(2796201, 3), 8388562, 12]-NRT-code), using
  - OOA 3-folding [i] 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(9⁹⁹, 2799486, F₉, 15, 11) (dual of [(2799486, 15), 41992191, 12]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row