In this article, some properties of the relative generalized Hamming weight (RGHW) of linear codes and their subcodes are developed with techniques in finite projective geometry. The relative generalized Hamming weights of almost all 4-dimensional q-ary linear codes and their subcodes are determined.

PurposeEpigenetic alterations have been investigated as prognostic indicators in breast cancer but their translation into clinical practice has been impeded by a lack of appropriate validation. We present the results of a meta-analysis of the associations between RASSF1A promoter methylation status and both disease free survival (DFS) and overall survival (OS) in female breast cancer.MethodsEligible studies were identified through searching the PubMed, Web of Science and Embase databases. Studies were pooled and summary hazard ratios (HR) with corresponding confidence intervals (CIs) were calculated. Funnel plots were also carried out to evaluate publication bias.ResultsA total of 1795 patients from eight studies were included in the meta-analysis. There are eight studies which investigated DFS in 1795 cases. The relative hazard estimates ranged from 1.77–5.64 with a combined HR of 2.75 (95%CI 1.96–3.84). The HR of RASSF1A promoter methylation on DFS adjusted for other potential prognostic factors was 2.54 (95%CI 1.77–3.66). There has been five trials which analyzed the associations of RASSF1A promoter methylation status with OS in 1439 patients. The hazard estimates ranged from 1.21–6.90 with a combined random-effects estimates of 3.47 (95%CI 1.44–8.34). OS reported in multivariate analysis was evaluated in four series comprising 1346 cases and the summarized random-effects HR estimate was 3.35 (95%CI 1.14–9.85). Additionally, no publication bias was detected for both OS and DFS.ConclusionThe results of this meta-analysis suggest that RASSF1A promoter hypermethylation confers a higher risk of relapse and a worse survival in patients with breast cancer. Large prospective studies are now needed to establish the clinical utility of RASSF1A promoter methylation.

The properties satisfied by the value function are given. These properties can be used to study the generalized Hamming weight and the relative generalized Hamming weight of certain linear codes.Keywords The value function · The generalized Hamming weight · Finite projective geometry · The relative generalized Hamming weight Mathematics Subject Classification (2000) 94B05