Manila Journal of Science 10 (2017), pp. 75-86

Sponsored Game With Fuzzy Coalitions

Abstract

Sponsorship is a way of expressing support where an individual or group gives provision (financial or in other forms) to an event, activity, person, or organization. When it comes to business, the two involved parties in a sponsorship are expected to engage in a mutual trading relationship so that each one expects to gain some benefit. In 2012, Nocon’s study introduced a game that models sponsorship, called sponsored game. In this type of game, there are two sets of players: the sponsors and the team players. Read More

On the Construction of Some LCD Codes over Finite Fields

On the Construction of Some LCD Codes over Finite Fields

Abstract

Linear codes with complementary duals (LCD codes) are linear codes that intersect with their duals trivially. In this paper, we construct some families of LCD codes using Massey’s characterization of an LCD code. In particular, we obtain some classes of binary LCD codes using the permutation matrix and the all-one matrix. We also explicitly construct generator matrices of LCD codes using the generator matrices of self-dual codes and binary Hamming codes. For, 3 r 7 the binary LCD codes obtained using the Hamming matrix Hr are optimal.  We also consider some known methods of combining two or more codes such as the direct product, direct sum, and Plotkin sum. We show that the direct product and the direct sum of two LCD codes are also LCD. We also prove that the permutation equivalence of codes preserves the LCD-ness of linear codes. Read More

Wee Nocon

Success Probability of an n-Step Process with n Independent Step Probabilities

Abstract

A process is defined as a series of actions or steps taken in order to achieve a particular end. Currently, there are a wide range of studies involving different types of processes ranging from engineering, business, biology, to information theory. We are interested in a new type of process study, labelled as Process Based Strategy Model. The process specifically looks into the success probability of an n-step process with n independent step probabilities. In our model, there are exactly n steps that lead to the desired goal Xn a success in step i leads to step i + 1 but a failure in it only leads to goal Xi – 1 and thereby, a failure in achieving the end goal Xn.

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