Algebraic Quantum Error-Correction Codes

Based on the group structure of a unitary Lie algebra, a scheme is provided to systematically and exhaustively generate quantum error correction codes, including the additive and nonadditive codes. The syndromes in the process of error-correction distinguished by different orthogonal vector subspaces, the coset subspaces. Moreover, the generated codes can be classified into four types with respect to the spinors in the unitary Lie algebra and a chosen initial quantum state

Reproductive biology of blue marlin (Makaira nigricans) in the western Pacific Ocean

The reproductive biology of blue marlin (Makaira nigricans) was assessed from 1001 fish (ranging from 121 to 275 cm in eye-to-fork length; EFL) caught by Taiwanese offshore longliners in the western Pacific Ocean from September 2000 to December 2001 and from 843 gonad samples from these fish, The overall sex ratio of the catch was approximately 1:1 dur ing the sampling period, but blue marlin are sexually dimorphic; females are larger than males. Reproductive activity (assessed by histology), a gonadosomatic index, and the distribution of oocyte diameters, indicated that spawning occurred predominantly from May to September. The estimated sizes-at-maturity (EFL50) were 179.76 ±1.01 cm (mean ±standard error) for females and 130 ±1 cm EFL for males. Blue marlin are multiple spawners and oocytes develop asynchronously. The proportion of mature females with ovaries containing postovulatory follicles (0.41) and hydrated oocytes (0.34) indicated that the blue marlin spawned once every 2–3 days on average. Batch fecundity (BF) for 26 females with the most advanced oocytes (≥1000 μm), but without postovulatory follicles, ranged from 2.11 to 13.50 million eggs (6.94 ± 0.54 million eggs). The relationships between batch fecundity (BF, in millions of eggs) and EFL and round weight (RW, kg) were BF = 3.29 × 10 –12 EFL5.31 (r2 = 0.70) and BF = 1.59 × 10–3 RW 1.73 (r2= 0.67), respectively. The parameters estimated in this study are key information for stock assessments of blue marlin in the western Pacific Ocean and will contribute to the conservation and sustainable yield o