This paper describes the calculation of the optimal partition parameters such that the girth maximum (m, r) Balanced Tanner Unit lies in family of BTUs specified by them using a series of proved results and thus creates a framework for specifying a search problem for finding the girth maximum (m, r) BTU. Several open questions for girth maximum (m, r) BTU have been raised.

Recently, we [1] proposed a simple-to-implement heuristic, namely, BIT-FILLING, for constructing high rate and high girth LDPC codes. In the present work, we extend BIT-FILLING, and demonstrate that the extended algorithm produces better codes, that is, codes with higher rate/girth and good bit error rate performance. We demonstrate the positive effect of girth on bit error rate performance.

in this paper, we consider a class of column-weight two quasi-cyclic low-density paritycheck codes in which the girth can be large enough, as an arbitrary multiple of 8. then we devote a convolutional form to these codes, such that their generator matrix can be obtained by elementary row and column operations on the parity-check matrix. finally, we show that the free distance of the convolution...

The girth of a finitely generated group G is defined to be the supremum of the girth of its Cayley graphs. Let G be a finitely generated subgroup of the mapping class group ModΣ, where Σ is an orientable closed surface with a finite number of punctures and with a finite number of components. We show that G is either a non-cyclic group with infinite girth or a virtually free-abelian group; these...

We investigate the basic interplay between the small k-valent vertex-transitive graphs of girth g and the (k, g)-cages, the smallest k-valent graphs of girth g. We prove the existence of k-valent Cayley graphs of girth g for every pair of parameters k ≥ 2 and g ≥ 3, improve the lower bounds on the order of the smallest (k, g) vertex-transitive graphs for certain families with prime power girth,...

Homomorphisms between graphs are studied as a generalization of colorings and of chromatic number. We investigate here homomorphisms from orienta-tions of undirected planar graphs to graphs (not necessarily planar) containing as few digons as possible. We relate the existence of such homomorphisms to girth and it appears that these questions remain interesting even under large girth assumption ...

The well-known Moore bound M(k, g) serves as a universal lower bound for the order of k-regular graphs of girth g. The excess e of a k-regular graph G of girth g and order n is the difference between its order n and the corresponding Moore bound, e = n −M(k, g). We find infinite families of parameters (k, g), g > 6 and even, for which we show that the excess of any k-regular graph of girth g is...

Girth weld cracking is one of the main failure modes in oil and gas pipelines; girth weld cracking inspection has great economic and social significance for the intrinsic safety of pipelines. This paper introduces the typical girth weld defects of oil and gas pipelines and the common nondestructive testing methods, and systematically generalizes the progress in the studies on technical principl...

We prove that every graph of minimum degree at least r and girth at least 186 contains a subdivision of Krþ1 and that for r5435 a girth of at least 15 suffices. This implies that the conjecture of Haj ! os that every graph of chromatic number at least r contains a subdivision of Kr (which is false in general) is true for graphs of girth at least 186 (or 15 if r5436). More generally, we show tha...