MinT - Information on Result #1566572

Information on Result #1566572

Linear OOA(128⁴¹, 7322, F₁₂₈, 3, 19) (dual of [(7322, 3), 21925, 20]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(128⁴¹, 7322, F₁₂₈, 2, 19) (dual of [(7322, 2), 14603, 20]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(128⁴¹, 8199, F₁₂₈, 2, 19) (dual of [(8199, 2), 16357, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(128⁴¹, 16398, F₁₂₈, 19) (dual of [16398, 16357, 20]-code), using
  - constructionÂ X applied to C_e(18) âŠ‚ C_e(13) [i] based on
    1. linear OA(128³⁷, 16384, F₁₂₈, 19) (dual of [16384, 16347, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    2. linear OA(128²⁷, 16384, F₁₂₈, 14) (dual of [16384, 16357, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
    3. linear OA(128⁴, 14, F₁₂₈, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,128)), using
      - discarding factors / shortening the dual code based on linear OA(128⁴, 128, F₁₂₈, 4) (dual of [128, 124, 5]-code or 128-arc in PG(3,128)), using
        Reedâ€“Solomon code RS(124,128) [i]

Mode: Linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n 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(128⁴¹, 2440, F₁₂₈, 21, 19) (dual of [(2440, 21), 51199, 20]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row