MinT - Information on Result #903108

Information on Result #903108

Linear OOA(49¹⁹, 2882452, F₄₉, 2, 5) (dual of [(2882452, 2), 5764885, 6]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(49², 50, F₄₉, 2, 2) (dual of [(50, 2), 98, 3]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;98,49) [i]
linear OOA(49¹⁷, 2882402, F₄₉, 2, 5) (dual of [(2882402, 2), 5764787, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(49¹⁷, 5764804, F₄₉, 5) (dual of [5764804, 5764787, 6]-code), using
  - discarding factors / shortening the dual code based on linear OA(49¹⁷, 5764805, F₄₉, 5) (dual of [5764805, 5764788, 6]-code), using
    - constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
      1. linear OA(49¹⁷, 5764801, F₄₉, 5) (dual of [5764801, 5764784, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
      2. linear OA(49¹³, 5764801, F₄₉, 4) (dual of [5764801, 5764788, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
      3. linear OA(49⁰, 4, F₄₉, 0) (dual of [4, 4, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(49⁰, s, F₄₉, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(49²⁴, 5764904, F₄₉, 2, 5) (dual of [(5764904, 2), 11529784, 6]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(49¹⁹, 2882451, F₄₉, 3, 5) (dual of [(2882451, 3), 8647334, 6]-NRT-code)	[i]	OOA Stacking with Additional Row
3	Linear OOA(49¹⁹, 2882451, F₄₉, 6, 5) (dual of [(2882451, 6), 17294687, 6]-NRT-code)	[i]	OOA Stacking with Additional Row