MinT - Information on Result #1192484

Information on Result #1192484

Digital (110, 132, 47664)-net over F₈, using net defined by OOA based on linear OOA(8¹³², 47664, F₈, 22, 22) (dual of [(47664, 22), 1048476, 23]-NRT-code), using

OA 11-folding and stacking [i] based on linear OA(8¹³², 524304, F₈, 22) (dual of [524304, 524172, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(8¹³², 524310, F₈, 22) (dual of [524310, 524178, 23]-code), using
  - trace code [i] based on linear OA(64⁶⁶, 262155, F₆₄, 22) (dual of [262155, 262089, 23]-code), using
    - constructionÂ X applied to C_e(21) âŠ‚ C_e(18) [i] based on
      1. linear OA(64⁶⁴, 262144, F₆₄, 22) (dual of [262144, 262080, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
      2. linear OA(64⁵⁵, 262144, F₆₄, 19) (dual of [262144, 262089, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
      3. linear OA(64², 11, F₆₄, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,64)), using
        discarding factors / shortening the dual code based on linear OA(64², 64, F₆₄, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
        Reedâ€“Solomon code RS(62,64) [i]

Mode: Constructive and linear.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (111, 133, 47664)-net over F₈	[i]		Net Duplication