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Planning for the Future : The Case of West Virginia
Dougherty, Michael John 한국국제지역사회개발학회 2001 地域社會開發學術誌 Vol.11 No.1
Proponents of planning have stressed the benefits that will accrue to the community as a rationale for the activity. This is a particularly strong incentive for planning, especially in places like West Virginia(USA) where planning at the county level has been sporadic. This study seeks to empirically prove the case for planning by showing that West Virginia counties that have undertaken planning have fared better with respect to "quality of life" and economic development factors than those counties that have not.
ADDITIVE SELF-DUAL CODES OVER FIELDS OF EVEN ORDER
Dougherty, Steven T.,Kim, Jon-Lark,Lee, Nari Korean Mathematical Society 2018 대한수학회보 Vol.55 No.2
We examine various dualities over the fields of even orders, giving new dualities for additive codes. We relate the MacWilliams relations and the duals of ${\mathbb{F}}_{2^{2s}}$ codes for these various dualities. We study self-dual codes with respect to these dualities and prove that any subgroup of order $2^s$ of the additive group is a self-dual code with respect to some duality.
HIGHER WEIGHTS AND GENERALIZED MDS CODES
Dougherty, Steven T.,Han, Sung-Hyu Korean Mathematical Society 2010 대한수학회지 Vol.47 No.6
We study codes meeting a generalized version of the Singleton bound for higher weights. We show that some of the higher weight enumerators of these codes are uniquely determined. We give the higher weight enumerators for MDS codes, the Simplex codes, the Hamming codes, the first order Reed-Muller codes and their dual codes. For the putative [72, 36, 16] code we find the i-th higher weight enumerators for i = 12 to 36. Additionally, we give a version of the generalized Singleton bound for non-linear codes.
OPTIMAL LINEAR CODES OVER ℤ<sub>m</sub>
Dougherty, Steven T.,Gulliver, T. Aaron,Park, Young-Ho,Wong, John N.C. Korean Mathematical Society 2007 대한수학회지 Vol.44 No.5
We examine the main linear coding theory problem and study the structure of optimal linear codes over the ring ${\mathbb{Z}}_m$. We derive bounds on the maximum Hamming weight of these codes. We give bounds on the best linear codes over ${\mathbb{Z}}_8$ and ${\mathbb{Z}}_9$ of lengths up to 6. We determine the minimum distances of optimal linear codes over ${\mathbb{Z}}_4$ for lengths up to 7. Some examples of optimal codes are given.
Codes over rings and Hermitian lattices
Dougherty, S.,Kim, J. L.,Lee, Y. Springer Science + Business Media 2015 Designs, codes, and cryptography Vol.76 No.3
<P>The purpose of this paper is to study a further connection between linear codes over three kinds of finite rings and Hermitian lattices over a complex quadratic field , where is a square free integer such that Shaska et al. (Finite Fields Appl 16(2): 75-87, 2010) consider a ring (p is a prime) and study Hermitian lattices constructed from codes over the ring . We consider a more general ring , where . Using allows us to make a connection from a code to a much larger family of lattices. That is, we are not restricted to those lattices whose minimum norm is less than p. We first show that is isomorphic to one of the following three non-isomorphic rings: a Galois ring , , and . We then prove that the theta functions of the Hermitian lattices constructed from codes over these three rings are determined by the complete weight enumerators of those codes. We show that self-dual codes over produce unimodular Hermitian lattices. We also discuss the existence of Hermitian self-dual codes over . Furthermore, we present MacWilliams' relations for codes over .</P>
HIGHER WEIGHTS AND GENERALIZED MDS CODES
Steven T. Dougherty,한성휴 대한수학회 2010 대한수학회지 Vol.47 No.6
We study codes meeting a generalized version of the Singleton bound for higher weights. We show that some of the higher weight enumerators of these codes are uniquely determined. We give the higher weight enumerators for MDS codes, the Simplex codes, the Hamming codes, the first order Reed-Muller codes and their dual codes. For the putative [72, 36, 16] code we find the i-th higher weight enumerators for i = 12 to 36. Additionally, we give a version of the generalized Singleton bound for non-linear codes.
Additive self-dual codes over fields of even order
Steven T. Dougherty,김종락,이나리 대한수학회 2018 대한수학회보 Vol.55 No.2
We examine various dualities over the fields of even orders, giving new dualities for additive codes. We relate the MacWilliams relations and the duals of $\FF_{2^{2s}}$ codes for these various dualities. We study self-dual codes with respect to these dualities and prove that any subgroup of order $2^s$ of the additive group is a self-dual code with respect to some duality.