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Supplementary figures and tables describing additional results and the datasets used in this study, respectively. (DOCX 5 kb)

The inactive X chromosome (Xi) in female mammals adopts an atypical higher-order chromatin structure, manifested as a global loss of local topologically associated domains (TADs), A/B compartments and formation of two mega-domains. Here we demonstrate that the non-canonical SMC family protein, SmcHD1, which is important for gene silencing on Xi, contributes to this unique chromosome architecture. Specifically, allelic mapping of the transcriptome and epigenome in SmcHD1 mutant cells reveals the appearance of sub-megabase domains defined by gene activation, CpG hypermethylation and depletion of Polycomb-mediated H3K27me3. These domains, which correlate with sites of SmcHD1 enrichment on Xi in wild-type cells, additionally adopt features of active X chromosome higher-order chromosome architecture, including A/B compartments and partial restoration of TAD boundaries. Xi chromosome architecture changes also occurred following SmcHD1 knockout in a somatic cell model, but in this case, independent of Xi gene derepression. We conclude that SmcHD1 is a key factor in defining the unique chromosome architecture of Xi., The inactive X chromosome (Xi) has an atypical structure, with global loss of TADs, A/B compartments and formation of mega-domains. Here the authors show that the non-canonical SMC family protein, SmcHD1, important for developmental gene silencing on Xi, antagonises TAD formation and compartmentalization on the Xi in a transcription independent way.

As a generalization of cyclic codes of length p^s over F_{p^a}, we study n-dimensional cyclic codes of length p^{s_1} X ... X p^{s_n} over F_{p^a} generated by a single "monomial". Namely, we study multi-variable cyclic codes of the form in F_{p^a}[x_1...x_n] / < x_1^{p^{s_1}}-1, ..., x_n^{p^{s_n}}-1 >. We call such codes monomial-like codes. We show that these codes arise from the product of certain single variable codes and we determine their minimum Hamming distance. We determine the dual of monomial-like codes yielding a parity check matrix. We also present an alternative way of constructing a parity check matrix using the Hasse derivative. We study the weight hierarchy of certain monomial like codes. We simplify an expression that gives us the weight hierarchy of these codes.

We study constacyclic codes, of length $np^s$ and $2np^s$, that are generated by the polynomials $(x^n + \gamma)^{\ell}$ and $(x^n - \xi)^i(x^n + \xi)^j$\ respectively, where $x^n + \gamma$, $x^n - \xi$ and $x^n + \xi$ are irreducible over the alphabet $\F_{p^a}$. We generalize the results of [5], [6] and [7] by computing the minimum Hamming distance of these codes. As a particular case, we determine the minimum Hamming distance of cyclic and negacyclic codes, of length $2p^s$, over a finite field of characteristic $p$., Comment: We do not plan to publish the results of this paper on their own. We have put this paper for referring purposes

We study cyclic codes of length 2p(s) over F-q where p is an odd prime. Using the results of [1], we compute the minimum Hamming distance of these codes.