MinT - Information on Result #1601863

Information on Result #1601863

Linear OOA(3⁷⁵, 2391500, F₃, 4, 8) (dual of [(2391500, 4), 9565925, 9]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3⁷⁵, 2391500, F₃, 2, 8) (dual of [(2391500, 2), 4782925, 9]-NRT-code), using

OOA 2-folding [i] based on linear OA(3⁷⁵, 4783000, F₃, 8) (dual of [4783000, 4782925, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(3⁷⁵, 4783001, F₃, 8) (dual of [4783001, 4782926, 9]-code), using
  - constructionÂ X applied to C_e(7) âŠ‚ C_e(4) [i] based on
    1. linear OA(3⁷¹, 4782969, F₃, 8) (dual of [4782969, 4782898, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
    2. linear OA(3⁴³, 4782969, F₃, 5) (dual of [4782969, 4782926, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
    3. linear OA(3⁴, 32, F₃, 2) (dual of [32, 28, 3]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁴, 40, F₃, 2) (dual of [40, 36, 3]-code), using
        Hamming code H(4,3) [i]

Mode: Linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3⁷⁵, 2391499, F₃, 5, 8) (dual of [(2391499, 5), 11957420, 9]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(3⁷⁵, 2391499, F₃, 12, 8) (dual of [(2391499, 12), 28697913, 9]-NRT-code)	[i]		OOA Stacking with Additional Row