Generalizing a way to construct Golay codes, codes of split type are defined. A lot of interesting codes, for example, extremal codes of length n ≤ 40 such as Golay codes and binary doubly even self-dual codes [48, 24, 12], [72, 36, w] with w ≥ 12, are represented as codes of split type.

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In the last decade, computable general equilibrium (CGE) models have emerged a standard tool for climate policy evaluation due to their abilities to prospectively elucidate the character and magnitude of the economic impacts of energy and environmental policies. Furthermore, marginal abatement cost (MAC) curves which represent GHG emissions reduction potentials and costs can be derived from these top-down economic models. However, most studies have never address MAC curves for a specific sector that have a large coverage of countries which are needed for allocation of optimal emission reductions. This paper aims to explicitly describe the meaning and character of MAC curves for transport sector in a CGE context through using the AIM/CGE Model developed by Toshihiko Masui. It found that the MAC curves derived in this study are the inverse of the general equilibrium reduction function for CO₂ emissions. Moreover, the transport sector MAC curves for six regions including USA, EU-15, Japan, China, India, and Brazil, derived from this study are compared to the reduction potentials under 100 USD/tCO₂ in 2020 from a bottom-up study. The results showed that the ranking of the regional reduction potentials in transport sector from this study are almost same with the bottom-up study except the ranks of the EU-15 and China. In addition, the range of the reduction potentials from this study is wider and only the USA has higher potentials than those derived from the bottom-up study.

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This is a rework of our old file on an explicit spectral decomposition of the mean value

$$M_2(g;A)=\int_{-\infty}^\infty{\left|{\zeta({\textstyle{1\over2}}+it)}\right|^{4}\left|{A({\textstyle{1\over2}}+it)}\right|^{2}g(t)dt}$$

that has been left unpublished since September 1994, though its summary account is given in [9] (see also [11, Section 4.6]); here

$$A(s)=\sum\limits_n{\alpha_{n}n^{-s}}$$

is a finite Dirichlet series and g is assumed to be even, regular, real-valued on R, and of fast decay on a sufficiently wide horizontal strip. On this occasion we add greater details as well as a rigorous treatment of the Mellin transform

$$Z_2(s;A)=\int_1^\infty{\left|{\zeta({\textstyle{1\over2}}+it)}\right|^{4}\left|{A({\textstyle{1\over2}}+it)}\right|^{2}t^{-s}dt}$$

which was scantly touched on in [9]. In particular, we specify the location of its poles and respective residues, under a mild condition on the coefficients $\alpha_n$.

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