MinT - Information on Result #1014345

Information on Result #1014345

Linear OOA(8⁹², 5597019, F₈, 3, 10) (dual of [(5597019, 3), 16790965, 11]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8¹⁸, 4617, F₈, 3, 5) (dual of [(4617, 3), 13833, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(8¹⁸, 4618, F₈, 2, 5) (dual of [(4618, 2), 9218, 6]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(8⁴, 585, F₈, 2, 2) (dual of [(585, 2), 1166, 3]-NRT-code), using
      - appending kth column [i] based on linear OA(8⁴, 585, F₈, 2) (dual of [585, 581, 3]-code), using
        Hamming code H(4,8) [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(8⁷⁴, 5592402, F₈, 3, 10) (dual of [(5592402, 3), 16777132, 11]-NRT-code), using
- trace code [i] based on linear OOA(64³⁷, 2796201, F₆₄, 3, 10) (dual of [(2796201, 3), 8388566, 11]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(64³⁷, large, F₆₄, 10) (dual of [large, large−37, 11]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(8⁹², 2798509, F₈, 15, 10) (dual of [(2798509, 15), 41977543, 11]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row