About Jarník’s-type relation in higher dimension

Gold type codes of higher relative dimension

or respectively 2 m−e 2e )d + 1, 2 m−3e 2e )d + 1, · · · , 2 m+3e 2e −k)d + 1. Then s1, · · · , sk−1 are maximum-length binary sequences of length 2 m − 1. Let C be the F2-vector space generated by all circular shifts of s, s1, · · · , sk−1. Then C has an F2m-vector space structure, and is of dimension k over F2m . When k = 2, C is the Gold code. So we regard C as a Gold type code of relative d...

Kasami type codes of higher relative dimension

Let m,n, d, e be fixed positive integers such that m = 2n, e = (n, d) = (m, d), 1 ≤ k ≤ n e . Let s be a fixed maximum-length binary sequence of length 2−1. For 0 ≤ j < k, let sj be the circular decimation of s with decimation factor 2 n e +1. Then s, s1, · · · , sk−1 are maximum-length binary sequences of length 2 − 1, while s0 is a maximum-length binary sequence of length 2−1. Let C be the F2...

Mirror Manifolds in Higher Dimension

We describe mirror manifolds in dimensions different from the familiar case of complex threefolds. We emphasize the simplifying features of dimension three and supply more robust methods that do not rely on such special characteristics and hence naturally generalize to other dimensions. The moduli spaces for Calabi–Yau d-folds are somewhat different from the “special Kähler manifolds” which had...

Gravitational Collapse in Higher Dimension

Spherically symmetric inhomogeneous dust collapse has been studied in higher dimensional spacetime and appearance of naked singularity has been analyzed both for non-marginal and marginally bound cases. It has been shown that naked singularity is possible for any arbitrary dimension in non-marginally bound case. For marginally bound case we have examined the radial null geodesics from the singu...

Convexity Ranks in Higher Dimension