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We construct a new family of permutationally invariant codes that correct $t$Pauli errors for any $t\ge 1$. We also show that codes in the new family correct quantum deletion errors as well as spontaneous decay errors. Our construction contains some of the previously known permutationally invariant quantum codes as particular cases, which also admit transversal gates. In many cases, the codes in the new family are shorter than the best previously known explicit permutationally invariant codes for Pauli errors and deletions. Furthermore, our new code family includes a new $\left(\right(4,2,2\left)\right)$optimal single-deletion-correcting code. As a separate result, we generalize the conditions for permutationally invariant codes to correct $t$Pauli errors from the previously known results for $t=1$to any number of errors. For small $t$, these conditions can be used to construct new examples of codes by computer. 

The SpTransformer (SpTrf) gene family in the purple sea urchin, Strongylocentrotus purpuratus, encodes immune response proteins. The genes are clustered, surrounded by short tandem repeats, and some are present in genomic segmental duplications. The genes share regions of sequence and include repeats in the coding exon. This complex structure is consistent with putative local genomic instability. Instability of the SpTrf gene cluster was tested by 10 days of growth of Escherichia coli harboring bacterial artificial chromosome (BAC) clones of sea urchin genomic DNA with inserts containing SpTrf genes. After the growth period, the BAC DNA inserts were analyzed for size and SpTrf gene content. Clones with multiple SpTrf genes showed a variety of deletions, including loss of one, most, or all genes from the cluster. Alternatively, a BAC insert with a single SpTrf gene was stable. BAC insert instability is consistent with variations in the gene family composition among sea urchins, the types of SpTrf genes in the family, and a reduction in the gene copy number in single coelomocytes. Based on the sequence variability among SpTrf genes within and among sea urchins, local genomic instability of the family may be important for driving sequence diversity in this gene family that would be of benefit to sea urchins in their arms race with marine microbes.