Permutation-invariant qudit codes from polynomials

A permutation-invariant quantum code on $N$ qudits is any subspace stabilized by the matrix representation of the symmetric group $S_N$ as permutation matrices that permute the underlying $N$ subsystems. When each subsystem is a complex Euclidean space of dimension $q \ge 2$, any permutation-invariant code is a subspace of the symmetric subspace of $(\mathbb C^q)^N.$ We give an algebraic construction of new families of of $d$-dimensional permutation-invariant codes on at least $(2t+1)^2(d-1)$ qudits that can also correct $t$ errors for $d \ge 2$. The construction of our codes relies on a real polynomial with multiple roots at the roots of unity, and a sequence of $q-1$ real polynomials that satisfy some combinatorial constraints. When $N > (2t+1)^2(d-1)$, we prove constructively that an uncountable number of such codes exist.Comment: 14 pages. Minor corrections made, to appear in Linear Algebra and its Application

"New Songs of the Battlefield": Songs and Memories of the Chinese Cultural Revolution

This dissertation focuses on a five-volume anthology of songs published from 1972 to 1976 known as "Zhandi Xinge," literally "New Songs of the Battlefield." The songs represent a significant portion of the limited musical expression during a period in China known as the Cultural Revolution (1966-76). Published and approved by the Chinese Communist Party, the anthology appeared at a time when artistic and musical activities were extremely restricted. The government utilized this particular musical form for multiple goals, including the propagation of political ideologies, stimulation of party support, and education of the masses. Based upon original research and personal interviews, the dissertation provides the first documentation and analysis of the anthology in any language. Analysis focuses on the official ideology as situated in its socio-historical context, and an examination of individual reception and memory. The study begins with an introduction to the Cultural Revolution period, followed by an investigation of the composition, editing, compilation, themes, texts, and musical characteristics of the anthology. The dissertation concludes with an analysis of the contemporary memory of Cultural Revolution songs while considering concepts of music, memory, and nostalgia. The analysis reveals that the major factors influencing how the music is remembered and who remembers it, is dependent upon a combination of features including music and memory, generational imprinting and changes in contemporary Chinese society