MinT - Information on Result #1014388

Information on Result #1014388

Linear OOA(8⁹⁹, 5596507, F₈, 3, 11) (dual of [(5596507, 3), 16789422, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8¹⁷, 4105, F₈, 3, 5) (dual of [(4105, 3), 12298, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(8¹⁷, 4106, F₈, 2, 5) (dual of [(4106, 2), 8195, 6]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(8³, 73, F₈, 2, 2) (dual of [(73, 2), 143, 3]-NRT-code), using
      - appending kth column [i] based on linear OA(8³, 73, F₈, 2) (dual of [73, 70, 3]-code), using
        Hamming code H(3,8) [i]
    2. linear OOA(8¹⁴, 4033, F₈, 2, 5) (dual of [(4033, 2), 8052, 6]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(8¹⁴, 8066, F₈, 5) (dual of [8066, 8052, 6]-code), using
        trace code [i] based on linear OA(64⁷, 4033, F₆₄, 5) (dual of [4033, 4026, 6]-code), using
        a code by Danev and Olsson [i]
linear OOA(8⁸², 5592402, F₈, 3, 11) (dual of [(5592402, 3), 16777124, 12]-NRT-code), using
- trace code [i] based on linear OOA(64⁴¹, 2796201, F₆₄, 3, 11) (dual of [(2796201, 3), 8388562, 12]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(64⁴¹, large, F₆₄, 11) (dual of [large, large−41, 12]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’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(8⁹⁹, 2798253, F₈, 15, 11) (dual of [(2798253, 15), 41973696, 12]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row