MinT - Information on Result #904862

Information on Result #904862

Linear OOA(128⁵⁰, 4202558, F₁₂₈, 2, 11) (dual of [(4202558, 2), 8405066, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(128⁹, 8257, F₁₂₈, 2, 5) (dual of [(8257, 2), 16505, 6]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(128², 129, F₁₂₈, 2, 2) (dual of [(129, 2), 256, 3]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;256,128) [i]
  2. linear OOA(128⁷, 8128, F₁₂₈, 2, 5) (dual of [(8128, 2), 16249, 6]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(128⁷, 16256, F₁₂₈, 5) (dual of [16256, 16249, 6]-code), using
      - discarding factors / shortening the dual code based on linear OA(128⁷, 16257, F₁₂₈, 5) (dual of [16257, 16250, 6]-code), using
        a code by Danev and Olsson [i]
linear OOA(128⁴¹, 4194301, F₁₂₈, 2, 11) (dual of [(4194301, 2), 8388561, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(128⁴¹, 8388602, F₁₂₈, 11) (dual of [8388602, 8388561, 12]-code), using
  - discarding factors / shortening the dual code based on linear OA(128⁴¹, large, F₁₂₈, 11) (dual of [large, large−41, 12]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 15790321Â | 128⁸âˆ’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(128⁵⁰, 2101279, F₁₂₈, 4, 11) (dual of [(2101279, 4), 8405066, 12]-NRT-code)	[i]		OOA Folding