The k-subset sum problem over finite fields is a classical NP-complete problem. Motivated by coding theory applications, a more complex problem is the higher m-th moment k-subset sum problem over finite fields. We show that there is a deterministic polynomial time algorithm for the m-th moment k-subset sum problem over finite fields for each fixed m when the evaluation set is the image set of a monomial or Dickson polynomial of any degree n. In the classical case m=1, this recovers previous results of Nguyen-Wang (the case m=1, p>2) [24] and the results of Choe-Choe (the case m=1, p=2) [3].

Objective

Hereditary myopathy with early respiratory failure (HMERF) is caused by titin A-band mutations in exon 344 and considered quite rare. Respiratory insufficiency is an early symptom. A collection of families and patients with muscle disease suggestive of HMERF was clinically and genetically studied.

Methods

Altogether 12 new families with 19 affected patients and diverse nationalities were studied. Most of the patients were investigated using targeted next-generation sequencing; Sanger sequencing was applied in some of the patients and available family members. Histological data and muscle MRI findings were evaluated.

Results

Three families had several family members studied while the rest were single patients. Most patients had distal and proximal muscle weakness together with respiratory insufficiency. Five heterozygous TTN A-band mutations were identified of which two were novel. Also with the novel mutations the muscle pathology and imaging findings were compatible with the previous reports of HMERF.

Conclusions

Our collection of 12 new families expands mutational spectrum with two new mutations identified. HMERF is not that rare and can be found worldwide, but maybe underdiagnosed. Diagnostic process seems to be complex as this study shows with mostly single patients without clear dominant family history.