MinT - Information on Result #1842096

Information on Result #1842096

OOA(128⁶³, 5969, S₁₂₈, 23, 23), using OOA 11-folding and stacking with additional row based on OA(128⁶³, 65660, S₁₂₈, 23), using

discarding factors based on OA(128⁶³, 65667, S₁₂₈, 23), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(128¹¹, 129, F₁₂₈, 11) (dual of [129, 118, 12]-code or 129-arc in PG(10,128)), using
    - extended Reedâ€“Solomon code RS_e(118,128) [i]
    - the expurgated narrow-sense BCH-code C(I) with length 129Â | 128²âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]
  2. OA(128⁵², 65538, S₁₂₈, 23), using
    - discarding parts of the base [i] based on linear OA(256⁴⁵, 65538, F₂₅₆, 23) (dual of [65538, 65493, 24]-code), using
      - constructionÂ X applied to C_e(22) âŠ‚ C_e(21) [i] based on
        linear OA(256⁴⁵, 65536, F₂₅₆, 23) (dual of [65536, 65491, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
        linear OA(256⁴³, 65536, F₂₅₆, 22) (dual of [65536, 65493, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
        linear OA(256⁰, 2, F₂₅₆, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(256⁰, s, F₂₅₆, 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.

Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	(40, 63, 5969)-net in base 128	[i]		Net Defined by OOA