MinT - Information on Result #910516

Information on Result #910516

Linear OOA(8¹⁶¹, 82, F₈, 2, 147) (dual of [(82, 2), 3, 148]-NRT-code), using juxtaposition based on

linear OOA(8⁹, 6, F₈, 2, 9) (dual of [(6, 2), 3, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8⁹, 8, F₈, 2, 9) (dual of [(8, 2), 7, 10]-NRT-code), using
  - Reedâ€“Solomon NRT-code RS(2;7,8) [i]
linear OOA(8¹⁴⁹, 76, F₈, 2, 137) (dual of [(76, 2), 3, 138]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(8⁹, 6, F₈, 2, 9) (dual of [(6, 2), 3, 10]-NRT-code) (see above)
  2. linear OOA(8¹³⁷, 70, F₈, 2, 127) (dual of [(70, 2), 3, 128]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(8⁷, 5, F₈, 2, 7) (dual of [(5, 2), 3, 8]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(8⁷, 8, F₈, 2, 7) (dual of [(8, 2), 9, 8]-NRT-code), using
        Reedâ€“Solomon NRT-code RS(2;9,8) [i]
      2. linear OOA(8¹²⁷, 65, F₈, 2, 119) (dual of [(65, 2), 3, 120]-NRT-code), using
        standard lengthening with (d₀,â€¦,d₁)Â = (118,119) [i] based on linear OOA(8¹²⁵, 64, F₈, 2, 117) (dual of [(64, 2), 3, 118]-NRT-code), using algebraic-geometric NRT-code AG(2;F,10P) with known gap numbers [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using the Suzuki function field over F₈ [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(8¹⁶¹, 82, F₈, 2, 146) (dual of [(82, 2), 3, 147]-NRT-code)	[i]		Strength Reduction for OOAs