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We define a family of codes called twisted Hermitian codes, which are based on Hermitian codes and inspired by the twisted Reed–Solomon codes described by Beelen, Puchinger, and Nielsen. We demonstrate that these new codes can have high-dimensional Schur squares, and we identify a subfamily of twisted Hermitian codes that achieves a Schur square dimension close to that of a random linear code. Twisted Hermitian codes allow one to work over smaller alphabets than those based on Reed–Solomon codes of similar lengths. [ABSTRACT FROM AUTHOR]

Disorganized morphogenesis of arteries, veins, capillaries, and lymphatic vessels results in vascular malformations. Most individuals with isolated vascular malformations have postzygotic (mosaic), activating pathogenic variants in a handful of oncogenes within the PI3K-RAS-MAPK pathway (Padia et al., Laryngoscope Investig Otolaryngol 4: 170-173 [2019]). Activating pathogenic variants in the gene PIK3CA , which encodes for the catalytic subunit of phosphatidylinositol 3-kinase, are present in both lymphatic and venous malformations as well as arteriovenous malformations in other complex disorders such as CLOVES syndrome (congenital, lipomatous, overgrowth, vascular malformations, epidermal anevi, scoliosis) (Luks et al., Pediatr Dev Pathol 16: 51 [2013]; Luks et al., J Pediatr 166: 1048-1054.e1-5 [2015]; Al-Olabi et al., J Clin Invest 128: 1496-1508 [2018]). These vascular malformations are part of the PIK3CA -related overgrowth spectrum, a spectrum of entities that have regionalized disordered growth due to the presence of tissue-restricted postzygotic PIK3CA pathogenic variants (Keppler-Noreuil et al., Am J Med Genet A 167A: 287-295 [2015]). Cerebrofacial vascular metameric syndrome (CVMS; also described as cerebrofacial arteriovenous metameric syndrome, Bonnet-Dechaume-Blanc syndrome, and Wyburn-Mason syndrome) is the association of retinal, facial, and cerebral vascular malformations (Bhattacharya et al., Interv Neuroradiol 7: 5-17 [2001]; Krings et al., Neuroimaging Clin N Am 17: 245-258 [2007]). The segmental distribution, the presence of tissue overgrowth, and the absence of familial recurrence are all consistent with CVMS being caused by a postzygotic mutation, which has been hypothesized by previous authors (Brinjiki et al., Am J Neuroradiol 39: 2103-2107 [2018]). However, the genetic cause of CVMS has not yet been described. Here, we present three individuals with CVMS and mosaic activating pathogenic variants within the gene PIK3CA We propose that CVMS be recognized as part of the PIK3CA -related overgrowth spectrum, providing justification for future trials using pharmacologic PIK3CA inhibitors (e.g., alpelisib) for these difficult-to-treat patients., (© 2021 Sheppard et al.; Published by Cold Spring Harbor Laboratory Press.)