@article {5226,
	title = {Asymptotic expansion of double Laplace-type integrals: The case of non-stationary minimum points},
	journal = {Proceedings of the American Mathematical Society},
	volume = {144},
	year = {2016},
	pages = {3741-3756},
	abstract = {In this paper, we show that the asymptotic expansion of a double Laplace-type integral with a non-stationary minimum point, located on the boundary of the domain of integration, is governed by the order of contact between the boundary curve and the level curve of the phase through the minimum point. This achievement will enable us to construct complete asymptotic expansions in more general settings. Especially, the problem will be completely solved if the phase and the boundary curve of the domain of integration are analytic near the minimum point.},
	author = {Nesrine Kamouche and Abdallah Benaissa}
}
@article {5229,
	title = {Simplex and MacDonald codes over Rq},
	journal = {Journal of Applied Mathematics and Computing},
	volume = {55},
	year = {2016},
	pages = {455{\textendash}478},
	abstract = {{ In this paper, we introduce the homogeneous weight and homogeneous Gray map over the ring\&nbsp;Rq=F2[u1,u2,{\textellipsis},uq]/⟨u2i=0},
	author = {Karima Chatouh and kenza Guenda and T. A Gulliver and Lemnouar Noui}
}
@article {5228,
	title = {On some classes of linear codes over Z2Z4 and their covering radii},
	journal = {Journal of Applied Mathematics and Computing},
	volume = {53},
	year = {2016},
	pages = {201{\textendash}222},
	abstract = {In this paper, we define the simplex and MacDonald codes of types\&nbsp;αα\&nbsp;and\&nbsp;β\&nbsp;over\&nbsp;Z2Z4. We also examine the covering radii of these codes. Further, we study the binary images of these codes and prove that the binary image of the simplex codes of type\&nbsp;αα\&nbsp;meets the Gilbert bound.},
	author = {Karima Chatouh and kenza Guenda and T Aaron Gulliver and Lemnouar Noui}
}
@article {5229,
	title = {Simplex and MacDonald codes over Rq},
	journal = {Journal of Applied Mathematics and Computing},
	volume = {55},
	year = {2016},
	pages = {455{\textendash}478},
	abstract = {
	In this paper, we introduce the homogeneous weight and homogeneous Gray map over the ring\&nbsp;Rq=F2[u1,u2,{\textellipsis},uq]/⟨u2i=0,uiuj=ujui⟩\&nbsp;for\&nbsp;q>=1q>=1. We also consider the construction of simplex and MacDonald codes of types\&nbsp;α\&nbsp;and\&nbsp;β\&nbsp;over this ring and their covering radius.

},
	author = {Karima Chatouh and kenza Guenda and T. A Gulliver and Lemnouar Noui}
}
@article {5228,
	title = {On some classes of linear codes over Z2Z4 and their covering radii},
	journal = {Journal of Applied Mathematics and Computing},
	volume = {53},
	year = {2016},
	pages = {201{\textendash}222},
	abstract = {
	In this paper, we define the simplex and MacDonald codes of types\&nbsp;αα\&nbsp;and\&nbsp;β\&nbsp;over\&nbsp;Z2Z4. We also examine the covering radii of these codes. Further, we study the binary images of these codes and prove that the binary image of the simplex codes of type\&nbsp;αα\&nbsp;meets the Gilbert bound.

},
	author = {Karima Chatouh and kenza Guenda and T Aaron Gulliver and Lemnouar Noui}
}
@article {5226,
	title = {Asymptotic expansion of double Laplace-type integrals: The case of non-stationary minimum points},
	journal = {Proceedings of the American Mathematical Society},
	volume = {144},
	year = {2016},
	pages = {3741-3756},
	abstract = {
	In this paper, we show that the asymptotic expansion of a double Laplace-type integral with a non-stationary minimum point, located on the boundary of the domain of integration, is governed by the order of contact between the boundary curve and the level curve of the phase through the minimum point. This achievement will enable us to construct complete asymptotic expansions in more general settings. Especially, the problem will be completely solved if the phase and the boundary curve of the domain of integration are analytic near the minimum point.

},
	author = {Nesrine Kamouche and Abdallah Benaissa}
}
