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The purpose of this paper is to study codes over finite principal ideal rings. To do this, we begin with codes over finite chain rings as a natural generalization of codes over Galois rings GR(p e , l) (including Z p e). We give sufficient conditions on the existence of MDS codes over finite chain rings and on the existence of self-dual codes over finite(More)
We construct new MDS or near-MDS self-dual codes over large finite fields. In particular, we show that there exists a Euclidean self-dual MDS code of length n = q over GF(q) whenever q = 2<sup>m</sup> (m ges 2) using a Reed-Solomon (RS) code and its extension. It turns out that this multiple description source (MDS) self-dual code is an extended duadic(More)
It is well known that the problem of finding stabilizer quantum-error-correcting codes (QECC) is transformed into the problem of finding additive self-orthogonal codes over the Galois field GF(4) under a trace inner product. Our purpose is to classify the extremal additive circulant self-dual codes of lengths up to 15, and construct good codes for lengths(More)
LDPC codes are serious contenders to Turbo codes in terms of decoding performance. One of the main problems is to give an explicit construction of such codes whose Tanner graphs have known girth. For a prime power q and m ≥ 2, Lazeb-nik and Ustimenko construct a q-regular bipartite graph D(m, q) on 2q m vertices, which has girth at least 2m/2 + 4. We regard(More)
Two class association schemes consist of either strongly regular graphs (SRG) or doubly regular tournaments (DRT). We construct self-dual codes from the adjacency matrices of these schemes. This generalizes the construction of Pless ternary Symmetry codes, Karlin binary Double Circulant codes, Calderbank and Sloane quaternary double circulant codes, and(More)
A binary code with the same weight distribution as its dual code is called formally self-dual (f.s.d.). We only consider f.s.d. even codes (codes with only even weight codewords). We show that any formally self-dual even binary code C of length n not divisible by 8 is balanced. We show that the weight distribution of a balanced near-extremal f.s.d. even(More)
—Our purpose is to find an upper bound for the length of s-extremal codes over F 2 (resp. F 4) when d ≡ 2 (mod 4) (resp. d odd). This question is left open in [6], [2]. More precisely, we show that if there is an [n, n 2 , d] s-extremal Type I binary self-dual code with d > 6 and d ≡ 2 (mod 4), then n < 21d − 82. Similarly we show that if there is an (n, 2(More)